Some Punctured Codes of Several Families of Binary Linear Codes
Some Punctured Codes of Several Families of Binary Linear Codes
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DOI：
10.1109/tit.2021.3088146
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发表时间：
2021-01
影响因子：
2.5
通讯作者：
Xiaoqiang Wang;Dabin Zheng;C. Ding
中科院分区：
文献类型：
--
作者：
Xiaoqiang Wang;Dabin Zheng;C. Ding
文献中已经广泛研究了具有有限域上函数的线性码的两种一般结构。第一个由 $\mathcal {C}(f)=\{ {\mathrm{ Tr}}({\textit{af}}({x})+{\textit{bx}})_{x \in \mathbb {F}_{q^{m}}^{*}} 给出： {a},{b} \in \mathbb {F}_{q^{m}} \}$ ，其中 ${q}$ 是素数幂， ${\mathbb F}_{q^{m}}^{*}= {\mathbb F}_{q^{m}} \setminus \{0\}$ ， Tr 是从 ${\mathbb F}_{q^{m}}$ 到 ${\mathbb F}_{q}$ 的迹函数，而 ${f}({x})$ 是来自 $\mathbb 的函数{F}_{q^{m}}$ 到 $\mathbb {F}_{q^{m}}$ 且 ${f}(0)=0$ 。第一次构造中使用了${\mathbb F}_{2^{m}}$上的几乎弯曲函数、二次函数和一些单项式，并且文献中获得了许多权重较少的二进制线性码族。本文研究了这些二进制码的一些删截码。本文得到了几个具有较少权重和新参数的二进制线性码族。本文还产生了几个具有新参数的距离最优二进制线性码族。
Two general constructions of linear codes with functions over finite fields have been extensively studied in the literature. The first one is given by $\mathcal {C}(f)=\{ {\mathrm{ Tr}}({\textit{af}}({x})+{\textit{bx}})_{x \in \mathbb {F}_{q^{m}}^{*}}: {a},{b} \in \mathbb {F}_{q^{m}} \}$ , where ${q}$ is a prime power, ${\mathbb F}_{q^{m}}^{*}= {\mathbb F}_{q^{m}} \setminus \{0\}$ , Tr is the trace function from ${\mathbb F}_{q^{m}}$ to ${\mathbb F}_{q}$ , and ${f}({x})$ is a function from $\mathbb {F}_{q^{m}}$ to $\mathbb {F}_{q^{m}}$ with ${f}(0)=0$ . Almost bent functions, quadratic functions and some monomials on ${\mathbb F}_{2^{m}}$ were used in the first construction, and many families of binary linear codes with few weights were obtained in the literature. This paper studies some punctured codes of these binary codes. Several families of binary linear codes with few weights and new parameters are obtained in this paper. Several families of distance-optimal binary linear codes with new parameters are also produced in this paper.