2006/09/29 by Maria Bras-Amorós, Bras-Amorós, Maria, Michael E. O’Sullivan +2
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Cryptographic Implementations and Security #Discrete Mathematics (cs.DM) #E.4 #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.DM #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.cs/0609162
Added references
openalex publication_date 2006/09/29 · arxiv created 2006/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Analysis of the Berlekamp-Massey-Sakata algorithm for decoding one-point codes leads to two methods for improving code rate. One method, due to Feng and Rao, removes parity checks that may be recovered by their majority voting algorithm. The second method is to design the code to correct only those error vectors of a given weight that are also geometrically generic. In this work, formulae are given for the redundancies of Hermitian codes optimized with respect to these criteria as well as the formula for the order bound on the minimum distance. The results proceed from an analysis of numerical semigroups generated by two consecutive integers. The formula for the redundancy of optimal Hermitian codes correcting a given number of errors answers an open question stated by Pellikaan and Torres in 1999.