New Construction of 2-Generator Quasi-Twisted Codes
Eric Z. Chen
TL;DR
This paper introduces a new explicit construction method for 2-generator quasi-twisted codes, resulting in many length-optimal and distance-optimal codes with potential applications in coding theory.
Contribution
It presents a novel construction of 2-generator QT codes based on consta-cyclic simplex codes, many of which meet the Griesmer bound and are thus optimal.
Findings
Many codes meet the Griesmer bound and are length-optimal.
New binary QC codes with specific parameters are constructed.
New ternary QC codes with specific parameters are obtained.
Abstract
Quasi-twisted (QT) codes are a generalization of quasi-cyclic (QC) codes. Based on consta-cyclic simplex codes, a new explicit construction of a family of 2-generator quasi-twisted (QT) two-weight codes is presented. It is also shown that many codes in the family meet the Griesmer bound and therefore are length-optimal. New distance-optimal binary QC [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, and good ternary QC [208, 6, 135] and [221, 6, 144] codes are also obtained by the construction.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications