On quadratic residue codes and hyperelliptic curves

2006/09/20 by David Joyner, Joyner, David
Computer Science · Mathematics · #11T71 #14G15 #14G50 #94B40 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #Cryptographic Implementations and Security #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #cs.IT #math.AG #math.CO #math.IT #math.NT #msc:11T71 #msc:14G15 #msc:14G50 #msc:94B40

paper · pdf · doi:10.48550/arxiv.math/0609562

18 pages, no figures

openalex publication_date 2006/09/20 · arxiv created 2008/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A long standing problem has been to develop "good" binary linear codes to be used for error-correction. This paper investigates in some detail an attack on this problem using a connection between quadratic residue codes and hyperelliptic curves. One question which coding theory is used to attack is: Does there exist a c<2 such that, for all sufficiently large p and all subsets S of GF(p), we have |X_S(GF(p))| < cp?

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