2003/06/03 by Gary McGuire, Jose Felipe Voloch, José Felipe Voloch +2
Computer Science · Mathematics · #11T71 #14H10 #94B15 #94B27 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:11T71 #msc:14H10 #msc:94B15 #msc:94B27
paper · pdf · doi:10.48550/arxiv.math/0306060
arxiv created 2003/06/03 · openalex publication_date 2003/06/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry, and an application of Weil's theorem. We relate the weights appearing in the dual codes to the number of rational points on a family of genus 2 curves over a finite field.