Some punctured codes of several families of binary linear codes
| Autor: | Dabin Zheng, Cunsheng Ding, Xiaoqiang Wang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
FOS: Computer and information sciences Monomial Computer Science - Information Theory Information Theory (cs.IT) Bent molecular geometry Function (mathematics) Quadratic function Library and Information Sciences Computer Science Applications Combinatorics Finite field Binary code Prime power Information Systems Projective geometry |
| DOI: | 10.48550/arxiv.2101.08425 |
| Popis: | Two general constructions of linear codes with functions over finite fields have been extensively studied in the literature. The first one is given by $\mathcal{C}(f)=\left\{ {\rm Tr}(af(x)+bx)_{x \in \mathbb{F}_{q^m}^*}: a,b \in \mathbb{F}_{q^m} \right\}$, where $q$ is a prime power, $\bF_{q^m}^*=\bF_{q^m} \setminus \{0\}$, $\tr$ is the trace function from $\bF_{q^m}$ to $\bF_q$, 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 $\bF_{2^m}$ 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. Comment: Boolean function, linear code, punctured code, distance-optimal code, weight distribution |
| Databáze: | OpenAIRE |
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