加性循环码与新量子码的多项式表示

IF 0.7 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI:10.3934/amc.2023036
Reza Dastbasteh, Khalil Shivji
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引用次数: 0

摘要

给出了$ \mathbb{F}_{p^2} $上的加性循环码的多项式表示。这种表示将被应用于通过最多两个生成器多项式唯一地表示每个加性循环码。我们确定了所有不同加性循环码的生成多项式。使用$ \mathbb{F}_p $上的线性循环码也提供了加性循环码的最小距离下界。我们对$ \mathbb{F}_{p^2} $上的所有辛自对偶、自正交和近自正交加性循环码进行了分类。最后,我们将量子结构应用于$ \mathbb{F}_{4} $上的自正交和近自正交加性循环码,得到了10个破纪录的二进制量子码。
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Polynomial representation of additive cyclic codes and new quantum codes
We give a polynomial representation for additive cyclic codes over $ \mathbb{F}_{p^2} $. This representation will be applied to uniquely present each additive cyclic code by at most two generator polynomials. We determine the generator polynomials of all different additive cyclic codes. A minimum distance lower bound for additive cyclic codes will also be provided using linear cyclic codes over $ \mathbb{F}_p $. We classify all the symplectic self-dual, self-orthogonal, and nearly self-orthogonal additive cyclic codes over $ \mathbb{F}_{p^2} $. Finally, we present ten record-breaking binary quantum codes after applying a quantum construction to self-orthogonal and nearly self-orthogonal additive cyclic codes over $ \mathbb{F}_{4} $.
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来源期刊
Advances in Mathematics of Communications
Advances in Mathematics of Communications 工程技术-计算机:理论方法
CiteScore
2.20
自引率
22.20%
发文量
78
审稿时长
>12 weeks
期刊介绍: Advances in Mathematics of Communications (AMC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not conform to these standards will be rejected. Areas covered include coding theory, cryptology, combinatorics, finite geometry, algebra and number theory, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in communications technology are welcome. More detailed indication of the journal''s scope is given by the subject interests of the members of the board of editors.
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