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two-weight codes and Second Order Recurrences

Chinese Journal of Electronics 2019年第6期28卷 1127-1130页

作者： SHI Minjia ZHANG Zhongyi SOLé Patrick Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Mathematical Sciences Anhui University School of Wendian Anhui University Aix Marseille Univ CNRS Centrale Marseile

Cyclic codes of dimension 2 over a finite field are shown to have at most two nonzero weights. We compute their weight distribution, and give a condition on the roots of their check polynomials for them to be maximum ... 详细信息

关键词： two-weight codes Irreducible Cyclic codes MDS codes Linear recurrences

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Optimal Ternary Cubic two-weight codes

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Chinese Journal of Electronics 2018年第4期27卷 734-738页

作者： SHI Minjia HUANG Daitao SOL Patrick Key Laboratory of Intelligent Computing & Signal Processing Ministry of EducationAnhui University School of Mathematical Sciences Anhui University CNRS/LAGA University of Paris 8

We study trace codes with defining set L,a subgroup of the multiplicative group of an extension of degree m of a certain ring of order 27. These codes are abelian, and their ternary images are quasi-cyclic of coindex three(a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when m is singly-even. When m is odd, under some hypothesises on the size of L, we obtain two new infinite families of two-weight codes which are optimal. Applications of the image codes to secret sharing schemes are also given.

关键词： Three-weight codes two-weight codes Gauss sums Trace codes

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One and two-weight Z2R2 Additive codes

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Chinese Journal of Electronics 2021年第1期30卷 72-76页

作者： LI Tiantian SHI Minjia LIN Bo WU Wenting School of Mathematical Sciences Anhui University School of Wendian Anhui University

This paper is devoted to the construction of one and two-weight Z2R2additive codes, where R2=F2[v]/(v~4). It is a generalization towards another direction of Z2Z4codes(S.T. Dougherty, H.W. Liu and L. Yu,"One weight Z2Z4additive codes", Applicable Algebra in Engineering, Communication and Computing, Vol.27,No.2, pp.123–138, 2016). A Mac Williams identity which connects the weight enumerator of an additive code over Z2R2and its dual is established. Several construction methods of one-weight and two-weight additive codes over Z2R2are presented. Several examples are presented to illustrate our main results and some open problems are also proposed.

关键词： Gray map One-weight codes two-weight codes Macwilliams identity

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codes From Strongly Regular (α,β)-reguli

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Journal of Shanghai Jiaotong university(Science) 2008年第4期13卷 491-494页

作者：李秀丽 Department of Mathematics Shanghai Jiaotong University

Strongly regular (α,β)-reguli are a class of incidence structures with given conditions which were introduced by Hamilton and Mathon. We introduce two classes of codes constructed from strongly regular (α,β)-regul... 详细信息

关键词： two-weight codes strongly regular (α,β)-reguli

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