Self-dual codes from circulant matrices

S. D. Georgiou; E. Lappas

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Self-dual codes from circulant matrices

机译：来自循环矩阵的自对偶代码

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摘要

In this paper, two general methods for constructing self-dual codes are presented. These methods use circulant matrices in circulant or bordered circulant structures to construct the suitable generator matrices. The necessary and sufficient conditions, for the generated codes to be self-dual, are provided. Special cases of the proposed methods include the well known "Pure Double Circulant" construction and the "Bordered Double circulant" construction of self-dual codes. As an example, the methods were applied to search for self-dual codes in GF(5). Many new inequivalent self-dual codes with best known distance are found.

机译：本文提出了两种构造自对偶码的通用方法。这些方法在循环或边界循环结构中使用循环矩阵来构造合适的生成器矩阵。提供了所生成的代码为自对偶的必要和充分条件。所提出的方法的特殊情况包括众所周知的“纯双循环”构造和自对码的“有界双循环”构造。例如，该方法被用于在GF（5）中搜索自对偶代码。发现了许多新的不等距的自我对偶码，它们之间的距离最为人所知。

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来源
《Designs, Codes and Crytography》 |2012年第2期|p.129-141|共13页
作者
S. D. Georgiou; E. Lappas;
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作者单位

Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Samos, Greece;

Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Samos, Greece;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
self-dual codes; circulant matrices; construction; periodic autocorrelationfunction;

机译：自对码;循环矩阵;施工;周期自相关函数;

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Self-dual codes from circulant matrices

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