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Constructions of Self-Orthogonal Codes From Hulls of BCH Codes and Their Parameters

机译：来自BCH代码的船体的自我正交码的结构及其参数

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摘要

Self-orthogonal codes are an interesting type of linear codes due to their wide applications in communication and cryptography. It is known that self-orthogonal codes are often used to construct quantum error-correcting codes, which can protect quantum information in quantum computations and quantum communications. Let C be an [n, k] cyclic code over F-q, where F-q is the finite field of order q. The hull of C is defined to be the intersection of the code and its dual. In this paper, we will employ the defining sets of cyclic codes to present two general characterizations of the hulls that have dimension k - 1 or k(perpendicular to) - 1, where k(perpendicular to) is the dimension of the dual code C-perpendicular to. Several sufficient and necessary conditions for primitive and projective BCH codes to have (k - 1)-dimensional (or (k(perpendicular to) - 1)-dimensional) hulls are also developed by presenting lower and upper bounds on their designed distances. Furthermore, several classes of self-orthogonal codes are proposed via the hulls of BCH codes and their parameters are also investigated. The dimensions and minimum distances of some self-orthogonal codes are determined explicitly. In addition, several optimal codes are obtained.
机译：由于它们在通信和密码学中的广泛应用，自正交码是一种有趣的线性码。众所周知，自正交码通常用于构造量子误差校正代码，其可以保护量子计算和量子通信中的量子信息。让C在F-Q上是一个[n，k]循环代码，其中f-q是有限的顺序q。 C的船体被定义为代码及其双重的交叉点。在本文中，我们将采用定义的循环码组，以呈现具有尺寸k - 1或k（垂直于）-1的船体的两种一般特征，其中k（垂直于）是双代码c的维度 - 垂直。还通过在其设计的距离上呈现下限和上限而产生的几种基本和投影BCH码的几种充分和必要的条件（K - 1） - 二维（或（k（垂直于） - 或（k（k（垂直于）-1）的船体。此外，通过BCH代码的船体提出了几种自我正交码，并且还研究了它们的参数。一些自我正交码的尺寸和最小距离是明确确定的。此外，获得了几种最佳代码。

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  • 来源
    《IEEE Transactions on Information Theory》 |2020年第11期|6774-6785|共12页
  • 作者

    Du Zongrun; Li Chengju; Mesnager Sihem;

  • 作者单位

    East China Normal Univ Shanghai Key Lab Trustworthy Comp Shanghai 200062 Peoples R China|State Key Lab Cryptol Beijing 100878 Peoples R China|Putian Univ Key Lab Appl Math Fujian Prov Univ Putian 351100 Peoples R China;

    East China Normal Univ Shanghai Key Lab Trustworthy Comp Shanghai 200062 Peoples R China|State Key Lab Cryptol Beijing 100878 Peoples R China|Putian Univ Key Lab Appl Math Fujian Prov Univ Putian 351100 Peoples R China;

    Univ Paris VIII Dept Math F-93526 St Denis France|Univ Sorbonne Paris Cite CNRS UMR 7539 Lab Anal Geometry & Applicat LAGA F-93430 Villetaneuse France|Telecom Paris Dept INFERES Res Grp MIC2 Math F-91120 Palaiseau France;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    Linear code; cyclic code; self-orthogonal code; hull; cyclotomic coset;

    机译：线性代码;循环代码;自我正交码;船体;紧固轴;

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