Some Punctured Codes of Several Families of Binary Linear Codes

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 C(f)={ Tr(af(x)+bx)x ∈ \mathbb Fqm*: a,b ∈ \mathbb Fqm }, where q is a prime power, \mathbb Fqm* = \mathbb Fqm \{0}, Tr is the trace function from \mathbb Fqm to \mathbb Fq, and f(x) is a function from \mathbb Fqm to \mathbb Fqm with f(0)=0. Almost bent functions, quadratic functions and some monomials on \mathbb F2m 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.