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Some Punctured Codes of Several Families of Binary Linear Codes.

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Title: Some Punctured Codes of Several Families of Binary Linear Codes.
Authors: Wang, Xiaoqiang, Zheng, Dabin, Ding, Cunsheng
Source: IEEE Transactions on Information Theory; Aug2021, Vol. 67 Issue 8, p5133-5148, 16p
Subject Terms: BINARY codes, LINEAR codes, BENT functions, FINITE fields, BOOLEAN functions, FAMILIES
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(ƒ) = {Tr(aƒ(x) + bx)x∈Fqm*: a, b ∈ Fqm}, where q is a prime power, Fqm* = Fqm \ {0}, Tr is the trace function from Fqm to Fq, and ƒ(x) is a function from Fqm to Fqm with ƒ(0) = 0. Almost bent functions, quadratic functions and some monomials on 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. [ABSTRACT FROM AUTHOR]
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Database: Complementary Index
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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(ƒ) = {Tr(aƒ(x) + bx)<subscript>x∈Fqm</subscript>*: a, b ∈ F<subscript>qm</subscript>}, where q is a prime power, F<subscript>qm</subscript>* = F<subscript>qm</subscript> \ {0}, Tr is the trace function from F<subscript>qm</subscript> to F<subscript>q</subscript>, and ƒ(x) is a function from F<subscript>qm</subscript> to F<subscript>qm</subscript> with ƒ(0) = 0. Almost bent functions, quadratic functions and some monomials on F<subscript>2m</subscript> 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. [ABSTRACT FROM AUTHOR]
ISSN:00189448
DOI:10.1109/TIT.2021.3088146