论文标题
二面体组代码的某些属性
Some properties of dihedral group codes
论文作者
论文摘要
在本文中，我们研究了二面代码，即$ \ mathbb {f} _qd_ {n} $的左理想，$ \ gcd（q，n）= 1 $。获得了二面代码及其双重的明确代数描述。此外，还获得了二面代码自二性的标准。构建了二面代码的基础，生成和检查矩阵。考虑到二面代码，我们考虑由环状代码引起的外部和内部代码。使用此代码，描述了生成矩阵的某些属性，并建立了与循环代码理论的连接。此外，获得了代码参数的一些估计值，并给出了一些说明性示例。
In this paper, we study the dihedral codes, i.e. the left ideals of $\mathbb{F}_qD_{n}$ in the case $\gcd(q, n) = 1$. An explicit algebraic description of the dihedral codes and their duals is obtained. In addition, a criterion for self-duality of a dihedral code is obtained. Bases, generating and check matrices of dihedral codes are constructed. Given a dihedral code, we consider exterior and interior codes that are induced by cyclic codes. Using this codes, some properties of generating matrices are described and a connection to cyclic code theory is established. In addition, some estimates of code parameters are obtained and several illustrative examples are given.
