Deng Tenghui, Yang Jing
Department of Mathematics, Tsinghua University, Beijing 100084, China.
College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China.
Entropy (Basel). 2024 Sep 20;26(9):803. doi: 10.3390/e26090803.
Let Fq be a finite field with an odd characteristic. In this paper, we present a new result about double cyclic codes over a finite non-chain ring. Specifically, we study the double cyclic code over Fq+vFq+v2Fq with v3=v, which is isomorphic to Fq×Fq×Fq. This study mainly involves generator polynomials and generator matrices. The generating polynomial of the dual code is also obtained. We show the relationship between the generating polynomials of the double cyclic codes and those of their dual codes. Finally, as an application of these results, we construct some optimal codes over F3.
设(F_q)为特征为奇数的有限域。在本文中，我们给出了关于有限非链环上双循环码的一个新结果。具体而言，我们研究了(F_q + vF_q + v^2F_q)上的双循环码，其中(v^3 = v)，它同构于(F_q×F_q×F_q)。该研究主要涉及生成多项式和生成矩阵。还得到了对偶码的生成多项式。我们展示了双循环码的生成多项式与其对偶码的生成多项式之间的关系。最后，作为这些结果的一个应用，我们构造了一些(F_3)上的最优码。
