The weight distributions of two classes of binary cyclic codes

Wang, Xiaoqiang; Zheng, Dabin; Hu, Lei; Zeng, Xiangyong

doi:10.1016/j.ffa.2015.01.012

Cited by 19 publications

(8 citation statements)

References 30 publications

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“…This is also a main method for constructing linear codes with few weights. The reader is referred to, for example, [7,20,26,33,39,43,51,57] for information.…”

Section: Introduction Of Motivations Objectives and Methodologymentioning

confidence: 99%

Some punctured codes of several families of binary linear codes

Wang

Zheng

Ding

2021

Preprint

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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∈F * q m : a, b ∈ F q m , where q is a prime power, F * q m = F q m \ {0}, Tr is the trace function from F q m to F q , and f (x) is a function from F q m to F q m with f (0) = 0. Almost bent functions, quadratic functions and some monomials on 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.

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“…This is also a main method for constructing linear codes with few weights. The reader is referred to, for example, [7,20,26,33,39,43,51,57] for information.…”

Section: Introduction Of Motivations Objectives and Methodologymentioning

confidence: 99%

Some punctured codes of several families of binary linear codes

Wang

Zheng

Ding

2021

Preprint

Self Cite

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“…, A n ) is an important research object in coding theory, as it contains crucial information about the error correcting capability of the code. Thus study on weight distribution of linear codes attracts much attention in coding theory and many works focus on determining weight distribution of linear codes (see, for example, [6,7,8,9,10,11,15,21,22,23,24] and the references therein). A code C is said to be a t-weight code if the number of nonzero A i in the sequence (A 1 , A 2 , • • • , A n ) is equal to t. Denote by C ⊥ the dual code of a linear code C. We call an [n, k, d] code distance-optimal if no [n, k, d + 1] code exists and dimensionoptimal if no [n, k + 1, d] code exists.…”

Section: Introductionmentioning

confidence: 99%

Some subfield codes from MDS codes

Xiang¹,

Luo²

2023

AMC

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<p style='text-indent:20px;'>Subfield codes of linear codes over finite fields have recently received a lot of attention, as some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, a class of binary subfield codes is constructed from a special family of MDS codes, and their parameters are explicitly determined. The parameters of their dual codes are also studied. Some of the codes presented in this paper are optimal or almost optimal.</p>

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“…The weight distribution of the duals of the cyclic codes with two zeros over finite fields of odd characteristic have been well investigated in [1, 2, 6, 7, 12, 19-22, 25, 27, 29], and the weight distribution of the dual of cyclic code with no less than three zeros can be found in [13,14,17,26,28,[30][31][32]. For cyclic codes with few nonzeros over finite fields of even characteristic, there are also some important results, including [15,18,23,24].…”

Section: Introductionmentioning

confidence: 99%

The weight distributions of constacyclic codes

Li¹,

Yue²,

Liu³

2017

Advances in Mathematics of Communications

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Let Fq be a finite field with q elements. Suppose that a, λ ∈ F * q , a n = λ with n|(q − 1). In this paper, we determine the weight distribution of a class of λ-constacyclic codes of length nm with the parity check polynomial h(x) = (x m − aξ st )(x m − aξ s(t+1) ) . . . (x m − aξ s(t+r−1) ) and n > (r − 1)m, where s, t, r are positive integers and ξ ∈ Fq is a primitive n-th root of unity. Moreover, we give the weight distributions of λ-constacyclic codes of length nm explicitly in several cases: (1) r = 1, n > 1; (2) r = 2, m = 2 and n > 2;(3) r = 2, m = 3 and n > 3; (4) r = 3, m = 2 and n > 4.

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The weight distributions of two classes of binary cyclic codes

Cited by 19 publications

References 30 publications

Some punctured codes of several families of binary linear codes

Some punctured codes of several families of binary linear codes

Some subfield codes from MDS codes

The weight distributions of constacyclic codes

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