We consider the basic theory of algebraic curves and their function fields necessary for constructing algebraic geometry codes and a pair of codes forming an error-correction pair which is used in a precomputation step of the decoding algorithm for the algebraic geometry codes. Also, we consider the decoding algorithm and give the necessary theory to prove its correctness. As a result, we consider elliptic curves, Hermitian curves and Klein quartics and construct the algebraic geometry codes associated with these families of curves, and also explicitly define the error-correcting pairs for the resulting codes.
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- Title Algebraic-geometry codes and decoding by error-correcting pairs
- Headline Algebraic-geometry codes and decoding by error-correcting pairs
- Publesher
Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 62
- Date:
- DOI 10.17223/20710410/62/7
Keywords
Klein quartic, Hermitian curve, elliptic curve, decoding of algebraic geometry code, error-correcting pair, function field, divisor, algebraic geometry codeAuthors
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Algebraic-geometry codes and decoding by error-correcting pairs | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2023. № 62. DOI: 10.17223/20710410/62/7
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