One-Generator Quasi-Abelian Codes Revisited
Somphong Jitman, Patanee Udomkavanich
TL;DR
This paper revisits 1-generator quasi-abelian codes over finite fields, providing new characterizations, an enumeration algorithm, and examples with improved minimum distances.
Contribution
It offers an explicit characterization, enumeration method, and concrete examples of 1-generator quasi-abelian codes with enhanced minimum distances.
Findings
Explicit characterization and enumeration algorithm for 1-generator quasi-abelian codes
Two codes with improved minimum distances from existing tables
New insights into the structure of quasi-abelian codes
Abstract
The class of 1-generator quasi-abelian codes over finite fields is revisited. Alternative and explicit characterization and enumeration of such codes are given. An algorithm to find all 1-generator quasi-abelian codes is provided. Two 1-generator quasi-abelian codes whose minimum distances are improved from Grassl's online table are presented.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications