Some punctured codes of several families of binary linear codes
Xiaoqiang Wang, Dabin Zheng, Cunsheng Ding

TL;DR
This paper investigates punctured versions of binary linear codes derived from functions over finite fields, resulting in new families of codes with few weights and optimal parameters, expanding the coding theory landscape.
Contribution
It introduces new punctured binary linear codes with few weights and optimal parameters, extending existing constructions with novel code families.
Findings
Several new families of binary linear codes with few weights.
New parameters for distance-optimal binary codes.
Enhanced code constructions using puncturing techniques.
Abstract
Two general constructions of linear codes with functions over finite fields have been extensively studied in the literature. The first one is given by , where is a prime power, , is the trace function from to , and is a function from to with . Almost bent functions, quadratic functions and some monomials on 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…
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · graph theory and CDMA systems
