Good Classical and Quantum Codes from Multi-Twisted Codes

TL;DR

This paper demonstrates how multi-twisted codes can be used to construct high-quality classical and quantum codes with desirable properties, offering more direct methods than previous approaches.

Contribution

It introduces new constructions of classical and quantum codes from multi-twisted codes, including optimal, reversible, and self-dual codes, with simpler methods than prior indirect approaches.

Findings

Obtained best known classical codes with good parameters.

Constructed new and best known non-binary quantum codes.

Developed theoretical results on binomials over finite fields.

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.