Land of Memories (Chinese: 机忆之地) is a Chinese science-fiction novel by Shen Yang (沈阳), a professor at Tsinghua University's School of Journalism and Communication. The story revolves around a former neuroscientist trying to recover her memories from the metaverse after suffering amnesia due to an accident. It contains almost 6,000 Chinese characters and was shortened from an AI-generated draft that was 43,000 characters long. The process involved 66 prompts spanning almost three hours. The novel was among 18 submissions that won the level-two prize at the Fifth Jiangsu Youth Science Education and Science Fiction Competition (第五届江苏省青年科普科幻作品大赛). The contest was restricted to participants between the age of 14 and 45 but did not forbid entries generated by AI. One of its organizers reached out to Shen after finding out that the professor had been experimenting with writing science fiction using AI. The judges were not told about the novel's origin in advance. Three of them, out of the six, approved the work. One judge, who had worked with AI models before, recognized that the novel was written by AI and criticized the work for lacking emotional appeal. The organizer who had contacted Shen said the novel's introduction was not bad but the story did not develop well. It would not meet the usual standards for publication. However, he still plans to allow AI-generated submissions in 2024. Fu Ruchu, editorial department director of the People's Literature Publishing House, said the novel was not easily identifiable as AI-generated and applauded its logical consistency. She warned that artificial intelligence could endanger the jobs of fiction writers and cause permanent damage to literary language.
Aggregation (linguistics)
In linguistics, aggregation is a subtask of natural language generation, which involves merging syntactic constituents (such as sentences and phrases) together. Sometimes aggregation can be done at a conceptual level. == Examples == A simple example of syntactic aggregation is merging the two sentences John went to the shop and John bought an apple into the single sentence John went to the shop and bought an apple. Syntactic aggregation can be much more complex than this. For example, aggregation can embed one of the constituents in the other; e.g., we can aggregate John went to the shop and The shop was closed into the sentence John went to the shop, which was closed. From a pragmatic perspective, aggregating sentences together often suggests to the reader that these sentences are related to each other. If this is not the case, the reader may be confused. For example, someone who reads John went to the shop and bought an apple may infer that the apple was bought in the shop; if this is not the case, then these sentences should not be aggregated. == Algorithms and issues == Aggregation algorithms must do two things: Decide when two constituents should be aggregated Decide how two constituents should be aggregated, and create the aggregated structure The first issue, deciding when to aggregate, is poorly understood. Aggegration decisions certainly depend on the semantic relations between the constituents, as mentioned above; they also depend on the genre (e.g., bureaucratic texts tend to be more aggregated than instruction manuals). They probably should depend on rhetorical and discourse structure. The literacy level of the reader is also probably important (poor readers need shorter sentences). But we have no integrated model which brings all these factors together into a single algorithm. With regard to the second issue, there have been some studies of different types of aggregation, and how they should be carried out. Harbusch and Kempen describe several syntactic aggregation strategies. In their terminology, John went to the shop and bought an apple is an example of forward conjunction Reduction Much less is known about conceptual aggregation. Di Eugenio et al. show how conceptual aggregation can be done in an intelligent tutoring system, and demonstrate that performing such aggregation makes the system more effective (and that conceptual aggregation make a bigger impact than syntactic aggregation). == Software == Unfortunately there is not much software available for performing aggregation. However the SimpleNLG system does include limited support for basic aggregation. For example, the following code causes SimpleNLG to print out The man is hungry and buys an apple.
Pamphlet war
A pamphlet war is a protracted argument or discussion through printed media, especially between the time the printing press became common, and when state intervention like copyright laws made such public discourse more difficult. The purpose was to defend or attack a certain perspective or idea. Pamphlet wars have occurred multiple times throughout history, as both social and political platforms. Pamphlet wars became viable platforms for this protracted discussion with the advent and spread of the printing press. Cheap printing presses, and increased literacy made the late 17th century a key stepping stone for the development of pamphlet wars, a period of prolific use of this type of debate. Over 2200 pamphlets were published between 1600–1715 alone. Pamphlet wars are generally credited for powering many key social changes of the era, including the Reformation and the Revolution Controversy, the English philosophical debate set off by the French Revolution. == History of the pamphlet in England == Throughout Europe in the 16th century, printed tracts were used to argue religious doctrine and foment support for religious causes. In England, Henry VIII used print literature to justify his break from the Catholic Church. During the subsequent reigns of Edward and Mary, print polemics escalated into propaganda warfare, as print media gained enormous potential to sway common opinion. By the 1560s, print was widely used to convey news. In 1562, the first pamphlets appeared, which discussed the English forces sent to aid the Protestant French Huguenots. In 1569, pamphlets reported the revolt of the Northern Earls and the subsequent Rebellion of the same year. In the 1580s, pamphlets began to replace broadsheet ballads as the means to convey information to the general public. Over the next century, the pamphlet became the principal means of garnering support for a cause or an idea, and was particularly influential during the English Civil Wars (1642-1651) and the Glorious Revolution of 1688. Through the ensuing decades, the pamphlet lost some popularity due to the emergence of newspapers and journals, but continued to be an important medium of public debate, as illustrated by the Revolution Controversy a full century later in the 1790s. == Pamphlet printing == Coming from a Latin word, "pamphlet" literally means "small book." In the early days of printing, the format of the book or pamphlet depended on the size of the paper used and the number of times it was folded. If a page was only folded once, it was called a folio. If it was folded twice, it was known as a quarto. An octave was a paper folded three times. A pamphlet was usually 1-12 sheets of paper folded in quarto, or 8-96 pages. It was sold for one or two pennies apiece. The printing of a pamphlet involved many people: the author, the printer, suppliers, print-makers, compositor, correctors, pressmen, binders, and distributors. Once the pamphleteer had written the pamphlet, it was sent to the printing house to be corrected, set into type, and printed. The papers were then given to the printer's warehouse-keeper, who bundled the copies and sent them to the bookseller, who was probably the one financing the printing. He was responsible to bind the pamphlets, usually by sewing them, and then sold them wholesale to individual bookselling vendors. The booksellers then sold them from a stall in the marketplace. == Pamphlet subjects == Pamphlets began as the means of conveyance for religious debates, and therefore religious topics were one of the main subjects they dealt with. The definition of a pamphlet came to mean a short work dealing with social, political, or religious issues. Typical topics included the Civil war, Church of England doctrines, Acts of Parliament, the Popish Plot (see below), the Stuart Era, and Cromwell propaganda. In addition, pamphlets were also used for romantic fiction, autobiography, scurrilous personal abuse, and social criticism. They contained much of the propaganda of the 17th century in the midst of the religious and political turmoil. They were also used for debates between the Puritans and the Anglican. During the Glorious Revolution, pamphlets were political weapons. == Authors == There were many authors of pamphlets. However some of the more popular authors include Daniel Defoe, Thomas Hobbes, Jonathan Swift, John Milton, and Samuel Pepys. Also included in the midst are Thomas Nashe, Joseph Addison, Richard Steele, and Matthew Prior. In 1591–1592, Robert Greene released a series of pamphlets which later inspired many other authors including Thomas Middleton and Thomas Dekker. == Critics == Pamphlets, along with their vast popularity, received criticism. There were many in the time period who believed that pamphlets were full of foolishness. They thought the pamphlets were not good enough literature and that they would turn people from "good" writing. They believed that pamphlets would be the end of the great volumes of literature and that great writing would be forgotten. == News reporting == Pamphlets made a great difference in the way news was reported to the general public. With the publication of pamphlets, it was no longer difficult for people to hear of events taking place far away. The closer the occurrence was to London, the easier and faster people heard of it. For example, the Battle of Edgehill took place on 23 October 1642. The first pamphlet reporting the incident was printed on 25 October 24 hours after some of the orders reported had been given. While not entirely accurate, and hurriedly made, the pamphlet nonetheless was able to tell the general public what had happened in the battle. A more accurate, specific, and readable account was available in a pamphlet printed on 26 October, and the "authorized" version was available only five days after the battle took place. == Marprelate pamphlets == In 1588, a series of pamphlets marked a turning point for the Puritans, dividing them from other Protestants in the country. The authors wrote under the pseudonym of Martin Marprelate and his two sons of the same name. The true identities of the authors were never discovered. The pamphlets aimed to provoke authorities to take action against censorship. The series was among the first to ask questions directly of its readers. == Early pamphlet wars == === Elizabethan pamphlet wars === As a means of forming or swaying public opinion, pamphlets like these had a part in influencing society, even as the content was itself influenced by society. During the 16th century and continuing for a short while in the early 17th century in England there was rise in the use of pamphlet wars to discuss a myriad of issues spanning from the civil war, to religious freedoms and the roles of women in society. The Queen herself participated in these discussions, making sure that she was widely read and understood by her people in order to gain favour and establish herself as the monarch despite being a woman. Examples of her use of this medium appear in To the Troops at Tilbury written in 1588, On Mary's Execution written in 1586, and many more. Another famous writer of this period to take advantage of the pamphlet was Emilia Lanier, famous for her arguments about the role of women. A common idea promoted by many literary works and the general attitude towards women, Lanier's work "Eve's Apology in Defence of Women" refuted the belief that Eve is responsible for the fall of man. A very uncommon and unpopular stance to take, Lanier accomplishes her defence through structuring it as an apology, one of the earliest subversive feminist texts. Similarly, Francis Bacon wrote his Essays to promote his idea of morality and other complicated social issues. For example, his work, "Of Love" examines the various understandings of the concept of love, particularly as it was perceived during the Elizabethan era. === Eikon Series === From 1649 until 1651, some five pamphlets were published in a debate about the execution of King Charles I of England (1600-1649). Prior to his execution, King Charles wrote the first pamphlet in the discussion, Eikon Basilike’’ (from the Greek “eikon” for image and “basileus” for king). The subtitle of this work - Portraiture of His Sacred Majesty in His Solitudes and Sufferings - indicates that Charles sought to portray himself as a martyr to the cause of regal prerogative. In the following months, several response pamphlets were published (collectively known as the "Eikon" series), including: Eikon Alethine, Eikon e Pistes, Eikonoklastes, and Eikon Aklastos,” alternately attacking or defending the king, his regicide, and his self-portrait in “Eikon Basilike.” == Popish Plot and Elizabeth Cellier == In the 1680s, after being acquitted of the "Meal-Tub Plot" for which she was accused, Elizabeth Cellier wrote Malice Defeated, which, along with The Matchless Picaro, sparked a pamphlet war surrounding debate of the ascension of a Catholic king to the thro
Web presence
A web presence is a location on the World Wide Web where a person, business, or some other entity is represented (see also web property and point of presence). Examples of a web presence for a person could be a personal website, a blog, a profile page, a wiki page, or a social media point of presence (e.g. a LinkedIn profile, a Facebook account, or a Twitter account). Examples of a web presence for a business or some other entity could be a corporate website, a microsite, a page on a review site, a wiki page, or a social media point of presence (e.g., a LinkedIn company page and/or group, a Facebook business/brand/product page, or a Twitter account). Every web presence is associated with a unique web address to distinguish one point of presence from another. == Owned vs. unowned == Web presence can either be owned or unowned. Owned media exists when a single person or group can control the content that is published on its web presence (e.g. a corporate website or a personal Twitter account). However, when a single person or group cannot solely control the content, the creator is different from the owner. This is considered unowned media (see earned media). A Wikipedia page or a Yelp page about a person, company, or product would be an example of a known (or "earned") web presence. Occasionally, a first form of media known as "paid media" is often included in the discussion of media types: "earned vs. owned vs. paid". Paid media is commonly found in the form of advertisements, but it is not considered a form of web presence. == Management == Web presence management is the process of establishing and maintaining a digital footprint on the web. The three factors that are considered include the following: where a person or business has web presence; how each web presence represents its enterprise; and what is published at a point of presence. Web presence management is the discipline of determining and governing: the distribution of policy documents which platforms are most appropriate (e.g. internal vs. external blog, YouTube vs. Vimeo) the single inventory of personal or corporate web presence (e.g. partners or advocates) where on the web a business and any relatable assets are represented where on the web a business and any relatable assets are impersonated or pirated web properties with the particular entities they represent who has control over which web properties new web properties which are not in the personal or corporate inventory (e.g. someone creates a new presence) authorized and unauthorized changes to the creation (e.g. branding) of a web presence a workflow for creating a web property that follows its corporate standards === Management system === The purpose of a web presence management system is to manage the web presence of a person or business. This includes the collection of domain names, websites, social media, and other web pages where he, she, or it is being represented. The tool generally offers the following key functions: new presence discovery, inventory management, change detection, access control, stakeholder coordination, and compliance workflow. A web presence management system is meant to have a broader reach so that it emphasizes where a presence has been established, will be established, must be maintained, or must be remediated. An example of a web presence management system is the Brandle Presence Manager. In order to publish content to the various points of web presence, multiple content management systems and sometimes even social media management systems are often used. The primary focus of most content and social media management systems is limited to their specific web platforms. === Domain names === Another aspect of web presence management is managing the collection of domain names registered to the person or business. Any entity may register multiple domain names for the same property. As a result, they can link alternative spellings, different top-level domains, aliases, brands, or products to the same website. Similarly, negative or derogatory domain names may also be registered. This is done to prevent certain domain names from being used against the person or business. It is common for a larger business to have domain names registered by multiple employees at multiple domain name registrars, possibly a result of organizational or geographical requirements. Consequently, a web presence management system can be used to monitor all domain names registered by the business, regardless of the registrars used. == Discovery == Web presence discovery is the process of monitoring the web for a new point of presence about a person or business. Web presence discovery is often included in a web presence management system. Whether a new domain is registered, a new website is published, or a new social media account is established, it occurs outside of the person's or business’ control. As a result, its purpose is to assess a new point of presence and appropriately handle any violations. Web presence discovery differs from content listening. The former involves looking for new properties on the web, whereas the latter refers to analyzing content that already exists to hear how a person or business is seen often in near real time. Examples of content listening systems include Sysomos and Radian6, which is now a subsidiary of Salesforce.com. === Brand protection === A person or business may choose to watch for a new web presence that might appear to misrepresent or mislead an audience, such as counterfeiters, spoofers, or malicious hackers. One of the early software in the online brand protection marketplace was MarkMonitor, now part of Thomson Reuters. This software helped detect rogue domain names and websites. However, the modern day growth of social media has seen a rise in the number of fraudulent brand impersonations. It has become much easier for a new web presence to be created on those platforms, which results in a greater frequency of them today. As a preventive measure, online brand protection providers are now adding social media to their domain and website discovery options. === Security === The widespread growth of social media has also made it easier for unauthorized individuals to impersonate an employee. Consequently, social media has now become a recognized threat vector in that it can be used to socially engineer an attack on a business. To counter this, companies are able to use web presence monitoring tools to detect new points of presence on the web and thereby defend against socially engineered attacks. === Distributed inventory management === A web presence monitoring system can be used by a business to associate a new web property with its corporate inventory. It is designed to address autonomous, distributed behaviors. This usually applies to larger businesses whose geographically diverse employees are more prone to creating new points of presence on the web. For example, a retail chain may allow each local store to create and manage their web presence to market to and communicate with their local customer base. Similarly, a global business may have teams in each country or region who create and manage a web presence to adapt to local languages or cultures. == Monitoring == Web presence monitoring is the process of monitoring a known inventory of web presence to detect any changes that are made. Web presence monitoring is often included in a web presence management system and can serve multiple purposes for both larger corporations and certain individuals, such as celebrities. It is important to note that presence monitoring differs from content listening. The former involves monitoring the properties (e.g. branding) of a web property in an established inventory, whereas the latter refers to analyzing content that already exists to hear how a person or business is seen often in near real time. Additionally, presence monitoring focuses on owned media and content listening on earned media. === Corporate, brand, and regulatory compliance === Many companies ensure that certain standards are met for a property on the web that represents their business. For companies in regulated industries, such as finance and healthcare, the company may be required by law to ensure that all publicized content, regardless of platform or technology, follow specific requirements. The widespread growth of social media has seen a rise in the number of fraudulent corporate impersonations. It has become much easier for a new web presence to be created on these platforms, and so these are much more prevalent than they used to be. As a preventive measure, a web presence monitoring system alerts the company when a known property is changed, allowing for the property to be reviewed and amended so that it follows the proper standards. . A web presence monitoring system helps alert the company when a known property is changed, so it can be reviewed and brought back, if necessary, into compliance with the appro
Social network hosting service
A social network hosting service is a web hosting service that specifically hosts the user creation of web-based social networking services, alongside related applications. Such services are also known as vertical social networks due to the creation of SNSes which cater to specific user interests and niches; like larger, interest-agnostic SNSes, such niche networking services may also possess the ability to create increasingly niche groups of users. == List of social network hosting services == Federated Media Publishing's BigTent BroadVision Clearvale Ning Wall.fm
Expectation propagation
Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as variational Bayesian methods. More specifically, suppose we wish to approximate an intractable probability distribution p ( x ) {\displaystyle p(\mathbf {x} )} with a tractable distribution q ( x ) {\displaystyle q(\mathbf {x} )} . Expectation propagation achieves this approximation by minimizing the Kullback–Leibler divergence K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} . Variational Bayesian methods minimize K L ( q | | p ) {\displaystyle \mathrm {KL} (q||p)} instead. If q ( x ) {\displaystyle q(\mathbf {x} )} is a Gaussian N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(\mathbf {x} |\mu ,\Sigma )} , then K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} is minimized with μ {\displaystyle \mu } and Σ {\displaystyle \Sigma } being equal to the mean of p ( x ) {\displaystyle p(\mathbf {x} )} and the covariance of p ( x ) {\displaystyle p(\mathbf {x} )} , respectively; this is called moment matching. == Applications == Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.
Locally recoverable code
Locally recoverable codes are a family of error correction codes that were introduced first by D. S. Papailiopoulos and A. G. Dimakis and have been widely studied in information theory due to their applications related to distributive and cloud storage systems. An [ n , k , d , r ] q {\displaystyle [n,k,d,r]_{q}} LRC is an [ n , k , d ] q {\displaystyle [n,k,d]_{q}} linear code such that there is a function f i {\displaystyle f_{i}} that takes as input i {\displaystyle i} and a set of r {\displaystyle r} other coordinates of a codeword c = ( c 1 , … , c n ) ∈ C {\displaystyle c=(c_{1},\ldots ,c_{n})\in C} different from c i {\displaystyle c_{i}} , and outputs c i {\displaystyle c_{i}} . == Overview == Erasure-correcting codes, or simply erasure codes, for distributed and cloud storage systems, are becoming more and more popular as a result of the present spike in demand for cloud computing and storage services. This has inspired researchers in the fields of information and coding theory to investigate new facets of codes that are specifically suited for use with storage systems. It is well-known that LRC is a code that needs only a limited set of other symbols to be accessed in order to restore every symbol in a codeword. This idea is very important for distributed and cloud storage systems since the most common error case is when one storage node fails (erasure). The main objective is to recover as much data as possible from the fewest additional storage nodes in order to restore the node. Hence, Locally Recoverable Codes are crucial for such systems. The following definition of the LRC follows from the description above: an [ n , k , r ] {\displaystyle [n,k,r]} -Locally Recoverable Code (LRC) of length n {\displaystyle n} is a code that produces an n {\displaystyle n} -symbol codeword from k {\displaystyle k} information symbols, and for any symbol of the codeword, there exist at most r {\displaystyle r} other symbols such that the value of the symbol can be recovered from them. The locality parameter satisfies 1 ≤ r ≤ k {\displaystyle 1\leq r\leq k} because the entire codeword can be found by accessing k {\displaystyle k} symbols other than the erased symbol. Furthermore, Locally Recoverable Codes, having the minimum distance d {\displaystyle d} , can recover d − 1 {\displaystyle d-1} erasures. == Definition == Let C {\displaystyle C} be a [ n , k , d ] q {\displaystyle [n,k,d]_{q}} linear code. For i ∈ { 1 , … , n } {\displaystyle i\in \{1,\ldots ,n\}} , let us denote by r i {\displaystyle r_{i}} the minimum number of other coordinates we have to look at to recover an erasure in coordinate i {\displaystyle i} . The number r i {\displaystyle r_{i}} is said to be the locality of the i {\displaystyle i} -th coordinate of the code. The locality of the code is defined as An [ n , k , d , r ] q {\displaystyle [n,k,d,r]_{q}} locally recoverable code (LRC) is an [ n , k , d ] q {\displaystyle [n,k,d]_{q}} linear code C ∈ F q n {\displaystyle C\in \mathbb {F} _{q}^{n}} with locality r {\displaystyle r} . Let C {\displaystyle C} be an [ n , k , d ] q {\displaystyle [n,k,d]_{q}} -locally recoverable code. Then an erased component can be recovered linearly, i.e. for every i ∈ { 1 , … , n } {\displaystyle i\in \{1,\ldots ,n\}} , the space of linear equations of the code contains elements of the form x i = f ( x i 1 , … , x i r ) {\displaystyle x_{i}=f(x_{i_{1}},\ldots ,x_{i_{r}})} , where i j ≠ i {\displaystyle i_{j}\neq i} . == Optimal locally recoverable codes == Theorem Let n = ( r + 1 ) s {\displaystyle n=(r+1)s} and let C {\displaystyle C} be an [ n , k , d ] q {\displaystyle [n,k,d]_{q}} -locally recoverable code having s {\displaystyle s} disjoint locality sets of size r + 1 {\displaystyle r+1} . Then An [ n , k , d , r ] q {\displaystyle [n,k,d,r]_{q}} -LRC C {\displaystyle C} is said to be optimal if the minimum distance of C {\displaystyle C} satisfies == Tamo–Barg codes == Let f ∈ F q [ x ] {\displaystyle f\in \mathbb {F} _{q}[x]} be a polynomial and let ℓ {\displaystyle \ell } be a positive integer. Then f {\displaystyle f} is said to be ( r {\displaystyle r} , ℓ {\displaystyle \ell } )-good if • f {\displaystyle f} has degree r + 1 {\displaystyle r+1} , • there exist distinct subsets A 1 , … , A ℓ {\displaystyle A_{1},\ldots ,A_{\ell }} of F q {\displaystyle \mathbb {F} _{q}} such that – for any i ∈ { 1 , … , ℓ } {\displaystyle i\in \{1,\ldots ,\ell \}} , f ( A i ) = { t i } {\displaystyle f(A_{i})=\{t_{i}\}} for some t i ∈ F q {\displaystyle t_{i}\in \mathbb {F} _{q}} , i.e., f {\displaystyle f} is constant on A i {\displaystyle A_{i}} , – # A i = r + 1 {\displaystyle \#A_{i}=r+1} , – A i ∩ A j = ∅ {\displaystyle A_{i}\cap A_{j}=\varnothing } for any i ≠ j {\displaystyle i\neq j} . We say that { A 1 , … , A ℓ {\displaystyle A_{1},\ldots ,A_{\ell }} } is a splitting covering for f {\displaystyle f} . === Tamo–Barg construction === The Tamo–Barg construction utilizes good polynomials. • Suppose that a ( r , ℓ ) {\displaystyle (r,\ell )} -good polynomial f ( x ) {\displaystyle f(x)} over F q {\displaystyle \mathbb {F} _{q}} is given with splitting covering i ∈ { 1 , … , ℓ } {\displaystyle i\in \{1,\ldots ,\ell \}} . • Let s ≤ ℓ − 1 {\displaystyle s\leq \ell -1} be a positive integer. • Consider the following F q {\displaystyle \mathbb {F} _{q}} -vector space of polynomials V = { ∑ i = 0 s g i ( x ) f ( x ) i : deg ( g i ( x ) ) ≤ deg ( f ( x ) ) − 2 } . {\displaystyle V=\left\{\sum _{i=0}^{s}g_{i}(x)f(x)^{i}:\deg(g_{i}(x))\leq \deg(f(x))-2\right\}.} • Let T = ⋃ i = 1 ℓ A i {\textstyle T=\bigcup _{i=1}^{\ell }A_{i}} . • The code { ev T ( g ) : g ∈ V } {\displaystyle \{\operatorname {ev} _{T}(g):g\in V\}} is an ( ( r + 1 ) ℓ , ( s + 1 ) r , d , r ) {\displaystyle ((r+1)\ell ,(s+1)r,d,r)} -optimal locally coverable code, where ev T {\displaystyle \operatorname {ev} _{T}} denotes evaluation of g {\displaystyle g} at all points in the set T {\displaystyle T} . === Parameters of Tamo–Barg codes === • Length. The length is the number of evaluation points. Because the sets A i {\displaystyle A_{i}} are disjoint for i ∈ { 1 , … , ℓ } {\displaystyle i\in \{1,\ldots ,\ell \}} , the length of the code is | T | = ( r + 1 ) ℓ {\displaystyle |T|=(r+1)\ell } . • Dimension. The dimension of the code is ( s + 1 ) r {\displaystyle (s+1)r} , for s {\displaystyle s} ≤ ℓ − 1 {\displaystyle \ell -1} , as each g i {\displaystyle g_{i}} has degree at most deg ( f ( x ) ) − 2 {\displaystyle \deg(f(x))-2} , covering a vector space of dimension deg ( f ( x ) ) − 1 = r {\displaystyle \deg(f(x))-1=r} , and by the construction of V {\displaystyle V} , there are s + 1 {\displaystyle s+1} distinct g i {\displaystyle g_{i}} . • Distance. The distance is given by the fact that V ⊆ F q [ x ] ≤ k {\displaystyle V\subseteq \mathbb {F} _{q}[x]_{\leq k}} , where k = r + 1 − 2 + s ( r + 1 ) {\displaystyle k=r+1-2+s(r+1)} , and the obtained code is the Reed-Solomon code of degree at most k {\displaystyle k} , so the minimum distance equals ( r + 1 ) ℓ − ( ( r + 1 ) − 2 + s ( r + 1 ) ) {\displaystyle (r+1)\ell -((r+1)-2+s(r+1))} . • Locality. After the erasure of the single component, the evaluation at a i ∈ A i {\displaystyle a_{i}\in A_{i}} , where | A i | = r + 1 {\displaystyle |A_{i}|=r+1} , is unknown, but the evaluations for all other a ∈ A i {\displaystyle a\in A_{i}} are known, so at most r {\displaystyle r} evaluations are needed to uniquely determine the erased component, which gives us the locality of r {\displaystyle r} . To see this, g {\displaystyle g} restricted to A j {\displaystyle A_{j}} can be described by a polynomial h {\displaystyle h} of degree at most deg ( f ( x ) ) − 2 = r + 1 − 2 = r − 1 {\displaystyle \deg(f(x))-2=r+1-2=r-1} thanks to the form of the elements in V {\displaystyle V} (i.e., thanks to the fact that f {\displaystyle f} is constant on A j {\displaystyle A_{j}} , and the g i {\displaystyle g_{i}} 's have degree at most deg ( f ( x ) ) − 2 {\displaystyle \deg(f(x))-2} ). On the other hand | A j ∖ { a j } | = r {\displaystyle |A_{j}\backslash \{a_{j}\}|=r} , and r {\displaystyle r} evaluations uniquely determine a polynomial of degree r − 1 {\displaystyle r-1} . Therefore h {\displaystyle h} can be constructed and evaluated at a j {\displaystyle a_{j}} to recover g ( a j ) {\displaystyle g(a_{j})} . === Example of Tamo–Barg construction === We will use x 5 ∈ F 41 [ x ] {\displaystyle x^{5}\in \mathbb {F} _{41}[x]} to construct [ 15 , 8 , 6 , 4 ] {\displaystyle [15,8,6,4]} -LRC. Notice that the degree of this polynomial is 5, and it is constant on A i {\displaystyle A_{i}} for i ∈ { 1 , … , 8 } {\displaystyle i\in \{1,\ldots ,8\}} , where A 1 = { 1 , 10 , 16 , 18 , 37 } {\displaystyle A_{1}=\{1,10,16,18,37\}} , A 2 = 2 A 1 {\displaystyle A_{2}=2A_{1}} , A 3 = 3 A 1 {\displaystyle A_{3}=3A_{1}} , A 4 = 4 A 1 {\displaystyle A_{4}=4A_{1}} , A 5 = 5 A 1 {\displaystyle A_{5}=5A_{1}} , A 6 = 6 A 1 {\displaystyle A_{6}=6A_{1}}