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Download as PDF; Printable version; In other projects ... This is a list of algebraic coding theory topics. ARQ; Adler-32; Algebraic geometry code ; BCH code; BCJR ...
The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched. [citation needed] Algebraic coding theory is basically divided into two major types of codes: [citation needed] Linear block codes; Convolutional codes
Algebraic geometry codes, often abbreviated AG codes, are a type of linear code that generalize Reed–Solomon codes. The Russian mathematician V. D. Goppa constructed these codes for the first time in 1982.
Download as PDF; Printable version; ... Pages in category "Coding theory" ... List of algebraic coding theory topics; A. Algebraic geometry code; Alternant code;
The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of all block codes in a unified way. Such limitations often take the form of bounds that relate different parameters of the block code to each other, such as its rate and its ability ...
This book is mainly centered around algebraic and combinatorial techniques for designing and using error-correcting linear block codes. [ 1 ] [ 3 ] [ 9 ] It differs from previous works in this area in its reduction of each result to its mathematical foundations, and its clear exposition of the results follow from these foundations.
The original algorithm uses binary Goppa codes (subfield codes of algebraic geometry codes of a genus-0 curve over finite fields of characteristic 2); these codes can be efficiently decoded, thanks to an algorithm due to Patterson. [4] The public key is derived from the private key by disguising the selected code as a general linear code.