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arXiv:2008.07037

Good Classical and Quantum Codes from Multi-Twisted Codes

Nuh Aydın, Thomas Guidotti, Peihan Liu

Published Aug 17, 2020• 1 citation
arXivHTMLPDF

Abstract

Multi-twisted (MT) codes were introduced as a generalization of quasi-twisted (QT) codes. QT codes have been known to contain many good codes. In this work, we show that codes with good parameters and desirable properties can be obtained from MT codes. These include best known and optimal classical codes with additional properties such as reversibility and self-duality, and new and best known non-binary quantum codes obtained from special cases MT codes. Often times best known quantum codes in the literature are obtained indirectly by considering extension rings. Our constructions have the advantage that we obtain these codes by more direct and simpler methods. Additionally, we found theoretical results about binomials over finite fields that are useful in our search.

DOI
10.48550/arxiv.2008.07037

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Recently, many good quantum codes over various finite fields FqF_qFq​ have been constructed from codes over extension rings or mixed alphabet rings via some version of a Gray map. We show that most of these codes can be obtained more directly from cyclic codes or their generalizations over FqF_qFq​. Unless explicit benefits are demonstrated for the indirect approach, we believe that direct and more elementary methods should be preferred.
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