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| 1 | Construction of One-Lee Weight and Two-Lee Weight Codes over IF_p+vIF_p显示文摘This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over IF_p+vIF_p(v^2=v) with type p^(2 k_1)p^(k2)p^(k3) based on two different distance-preserving Gray maps from((IF_p+vIF_p)~n, Lee weight) to(IF_p^(2 n), Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p=2. | SHI Minjia LUO Yong SOLE Patrick | 2017 | Journal of Systems Science & Complexity2017，30，2： | 2 |
| 2 | Skew Cyclic Codes over a Non-chain Ring显示文摘We study skew cyclic codes over a nonchain ring,which generalizes our previous results in IEICE Trans.on Fundamentals of Electronic Communications and Computer Sciences,2015.We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over the ring by a decomposition theorem.The generator polynomial of the dual code of a skew cyclic code are obtained.Moreover,the idempotent generators of skew cyclic codes are considered.Some examples are also presented to illustrate the discussed results. | SHI Minjia YAO Ting SOLE Patrick | 2017 | Chinese Journal of Electronics2017，26，3： | 2 |
| 3 | Two-Weight Codes and Second Order Recurrences显示文摘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 distance separable code. | SHI Minjia ZHANG Zhongyi SOLE Patrick | 2019 | Chinese Journal of Electronics2019，28，6： | 0 |
| 4 | Optimal Ternary Cubic Two-Weight Codes显示文摘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. | SHI Minjia HUANG Daitao SOLE Patrick | 2018 | Chinese Journal of Electronics2018，27，4： | 0 |
| 5 | An Analogue of the Z4-Goethals Code in Non-Primitive Length显示文摘This paper constructs a cyclic Z_4-code with a parity-check matrix similar to that of Goethals code but in length 2~m+ 1, for all m ≥ 4. This code is a subcode of the lifted Zetterberg code for m even. Its minimum Lee weight is shown to be at least 10, in general, and exactly 12 in lengths 33, 65. The authors give an algebraic decoding algorithm which corrects five errors in these lengths for m = 5, 6 and four errors for m > 6. | ALAHMADI Adel ALHAZMI Husain ALI Shakir HELLESETH Tor HIJAZI Rola LI Chunlei SOLE Patrick | 2017 | Journal of Systems Science & Complexity2017，30，4： | 0 |
| 6 | The Adjacency Codes of the First Yellow Graphs显示文摘The authors study the binary codes spanned by the adjacency matrices of the strongly regular graphs(SRGs)on at most two hundred vertices whose existence is unknown.The authors show that in length less than one hundred they cannot be cyclic,except for the exceptions of the SRGs of parameters(85,42,20,21)and(96,60,38,36).In particular,the adjacency code of a(85,42,20,21)is the zero-sum code.In the range[100,200]the authors find 29 SRGs that could possibly have a cyclic adjacency code. | SHI Minjia LI Shitao KIM Jon-Lark SOLE Patrick | 2023 | Journal of Systems Science & Complexity2023，36，4： | 0 |
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