Decoding up to 4 errors in Hyperbolic-like Abelian Codes by the Sakata\n Algorithm

2020/07/17 by José Joaquín Bernal, Juan Jacobo Simón, Bernal, José Joaquín +1 · 1 citation
Computer Science · #Algorithms and Data Compression #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.2007.09039

openalex publication_date 2020/07/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We deal with two problems related with the use of the Sakata's algorithm in a\nspecific class of bivariate codes. The first one is to improve the general\nframework of locator decoding in order to apply it on such abelian codes. The\nsecond one is to find a set of indexes oF the syndrome table such that no other\nsyndrome contributes to implement the BMSa and, moreover, any of them may be\nignored \a priori. In addition, the implementation on those indexes is\nsufficient to get the Groebner basis; that is, it is also a termination\ncriterion.\n

Cited by

• Hyperbolic Sets in Incomplete Tables

Related

• Inference of unknown syndrome values in the implementation of the Berlekamp-Massey-Sakata algorithm
• Inverse-free Berlekamp-Massey-Sakata Algorithm and Small Decoders for Algebraic-Geometric Codes
• On Semigroups Generated by Two Consecutive Integers and Improved Hermitian Codes
• Apparent Distance and a Notion of BCH Multivariate Codes
• On decoding hyperbolic codes