论文标题
使用简单复合物的线性代码
Linear codes using simplicial complexes
论文作者
论文摘要
某些简单络合物用于构建子集$ d $的$ \ mathbb {f} _ {2^n}^m $和$ d $，进而定义线性代码$ c_ {d} $ over $ \ mathbb {f} _ {2^n} $ cy y IN $（v \ cdot d） \ Mathbb {f} _ {2^n}^m $。在这里，我们处理案例$ n = 3 $，也就是说，当$ c_ {d} $是八章代码时。我们在生成器矩阵的帮助下，建立了$ c_ {d} $与其二进制子场代码$ c_ {d}^{（2）} $之间的关系。对于给定的长度和尺寸，如果代码具有最高的距离，则称为距离最佳。关于Griesmer结合，获得了五个无限的距离最佳代码家族，并建立了某些线性代码的足够条件。
Certain simplicial complexes are used to construct a subset $D$ of $\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over $\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in \mathbb{F}_{2^n}^m$. Here we deal with the case $n=3$, that is, when $C_{D}$ is an octanary code. We establish a relation between $C_{D}$ and its binary subfield code $C_{D}^{(2)}$ with the help of a generator matrix. For a given length and dimension, a code is called distance optimal if it has the highest possible distance. With respect to the Griesmer bound, five infinite families of distance optimal codes are obtained, and sufficient conditions for certain linear codes to be minimal are established.
