A Generalization of the ASR Search Algorithm to 2-Generator Quasi-Twisted Codes
Abstract
One of the main goals of coding theory is to construct codes with best possible parameters and properties. A special class of codes called quasi-twisted (QT) codes is well-known to produce codes with good parameters. Most of the work on QT codes has been over the 1-generator case. In this work, we focus on 2-generator QT codes and generalize the ASR algorithm that has been very effective to produce new linear codes from 1-generator QT codes. Moreover, we also generalize a recent algorithm to test equivalence of cyclic codes to constacyclic codes. This algorithm makes the ASR search even more effective. As a result of implementing our algorithm, we have found 103 QT codes that are new among the class of QT codes. Additionally, most of these codes possess the following additional properties: a) they have the same parameters as best known linear codes, and b) many of the have additional desired properties such as being LCD and dual-containing. Further, we have also found a binary 2-generator QT code that is new (record breaking) among all binary linear codes and its extension yields another record breaking binary linear code.
Cite
@article{arxiv.2108.10316,
title = {A Generalization of the ASR Search Algorithm to 2-Generator Quasi-Twisted Codes},
author = {Dev Akre and Nuh Aydin and Matthew J. Harrington and Saurav R. Pandey},
journal= {arXiv preprint arXiv:2108.10316},
year = {2021}
}