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New classes of binary few weight codes from trace codes over a chain ring

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Abstract

In this paper, we construct several infinite families of codes over the chain ring \(R={\mathbb {F}}_2[u]/\langle u^k\rangle \), i.e., \(R={\mathbb {F}}_2+u{\mathbb {F}}_2+\cdots +u^{k-1}{\mathbb {F}}_2, u^{k}=0\) by employing simplicial complexes. When the simplicial complexes are all generated by a single maximal element, we compute the homogeneous weight distributions of these classes of codes. By the Gray map, we obtain that some classes of codes are minimal and some classes of these codes are distance optimal. The codewords of these codes are shown to be minimal for inclusion of supports, a fact favorable to an application to secret sharing schemes.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Xiaoxiao Li & Minjia Shi

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  1. Xiaoxiao Li
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  2. Minjia Shi
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Correspondence to Minjia Shi.

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This research is supported by the National Natural Science Foundation of China (12071001, 61672036), the Excellent Youth Foundation of Natural Science Foundation of Anhui Province (1808085J20), the Academic Fund for Outstanding Talents in Universities (gxbjZD03).

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Li, X., Shi, M. New classes of binary few weight codes from trace codes over a chain ring. J. Appl. Math. Comput. 68, 1869–1880 (2022). https://doi.org/10.1007/s12190-021-01549-2

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  • DOI: https://doi.org/10.1007/s12190-021-01549-2

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