关于斜拟循环码的推广

IF 0.5 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2020-01-01 DOI:10.4134/BKMS.B190325

Sumeyra Bedir, F. Gursoy, I. Siap

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引用次数: 2

摘要

在过去的二十年中，非交换环上的码已成为编码理论的主要趋势之一。由于非交换性在本质上带来了许多具有挑战性的问题，仍然有许多开放的问题需要解决。2015年，Matsui研究了广义拟循环(GQC)码的生成多项式矩阵和奇偶校验多项式矩阵。我们将这些结果推广到非交换的情况。研究了偏常环码的对偶结构，给出了一种直接获得偏多扭码的奇偶校验多项式的方法。在此基础上，给出了偏多环码及其对偶的代数结构，并给出了一些例子来说明这些定理。

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ON GENERALIZATIONS OF SKEW QUASI-CYCLIC CODES

In the last two decades, codes over noncommutative rings have been one of the main trends in coding theory. Due to the fact that noncommutativity brings many challenging problems in its nature, still there are many open problems to be addressed. In 2015, generator polynomial matrices and parity-check polynomial matrices of generalized quasi-cyclic (GQC) codes were investigated by Matsui. We extended these results to the noncommutative case. Exploring the dual structures of skew constacyclic codes, we present a direct way of obtaining parity-check polynomials of skew multi-twisted codes in terms of their generators. Further, we lay out the algebraic structures of skew multipolycyclic codes and their duals and we give some examples to illustrate the theorems.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).