Additive twisted codes: new distance bounds and infinite families of quantum codes

IF 1.2 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Designs, Codes and Cryptography Pub Date : 2025-01-16 DOI:10.1007/s10623-024-01552-1

Reza Dastbasteh, Petr Lisoněk

引用次数: 0

Abstract

We provide a new construction of quantum codes that enables integration of a broader class of classical codes into the mathematical framework of quantum stabilizer codes. Next, we present new connections between twisted codes and linear cyclic codes and provide novel bounds for the minimum distance of twisted codes. We show that classical tools such as the Hartmann–Tzeng minimum distance bound are applicable to twisted codes. This enabled us to discover five new infinite families and many other examples of record-breaking, and sometimes optimal, binary quantum codes. We also discuss the role of the \(\gamma \) value on the parameters of twisted codes and present new results regarding the construction of twisted codes with different \(\gamma \) values but identical parameters. Finally, we list many new record-breaking binary quantum codes that we obtained from additive twisted, linear cyclic, and constacyclic codes.

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加性扭曲码：新的距离边界和量子码的无限族

我们提供了一种新的量子码结构，可以将更广泛的经典码集成到量子稳定码的数学框架中。在此基础上，提出了双扭码与线性循环码之间的新联系，并给出了双扭码最小距离的新界限。我们证明了Hartmann-Tzeng最小距离界等经典工具适用于扭曲码。这使我们发现了五个新的无限族和许多其他破纪录的例子，有时是最佳的，二进制量子代码。我们还讨论了\(\gamma \)值对扭曲码参数的作用，并给出了关于\(\gamma \)值不同但参数相同的扭曲码的构造的新结果。最后，我们列举了从加性扭曲码、线性循环码和恒循环码中获得的许多新的破纪录二进制量子码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.