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Two Classes of Constacyclic Codes with Variable Parameters

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Arithmetic of Finite Fields (WAIFI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13638))

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Abstract

Constacyclic codes over finite fields are a family of linear codes and contain cyclic codes as a subclass. Constacyclic codes are closely related to many areas of mathematics and outperform cyclic codes in several aspects. Hence, constacyclic codes are of theoretical importance. On the other hand, constacyclic codes are important in practice, as they have rich algebraic structures and may have efficient decoding algorithms. In this extended abstract, two classes of constacyclic codes are constructed using a general construction of constacyclic codes with cyclic codes. The first class of constacyclic codes is motivated by the punctured Dilix cyclic codes, and the second class is motivated by the punctured generalised Reed-Muller codes. The two classes of constacyclic codes contain optimal linear codes. The parameters of the two classes of constacyclic codes are analysed, and some open problems are presented in this extended abstract.

C. Ding’s research was supported by The Hong Kong Research Grants Council, Proj. No. 16301522, Z. Sun’s research was supported by The National Natural Science Foundation of China under Grant Number 62002093. X. Wang’s research was supported by The National Natural Science Foundation of China under Grant Number 12001175.

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Acknowledgements

The first author thanks Sihem Mesnager and Zhengchun Zhou for inviting him to present the talk at WAIFI 2022.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Cunsheng Ding

  2. School of Mathematics, Hefei University of Technology, Hefei, 230601, Anhui, China

    Zhonghua Sun

  3. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Xiaoqiang Wang

Authors
  1. Cunsheng Ding
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  2. Zhonghua Sun
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  3. Xiaoqiang Wang
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Correspondence to Cunsheng Ding .

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Editors and Affiliations

  1. Department of Mathematics, University of Paris VIII, Paris, France

    Sihem Mesnager

  2. School of Mathematics, Southwest Jiaotong University, Chengdu, China

    Zhengchun Zhou

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Ding, C., Sun, Z., Wang, X. (2023). Two Classes of Constacyclic Codes with Variable Parameters. In: Mesnager, S., Zhou, Z. (eds) Arithmetic of Finite Fields. WAIFI 2022. Lecture Notes in Computer Science, vol 13638. Springer, Cham. https://doi.org/10.1007/978-3-031-22944-2_7

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  • DOI: https://doi.org/10.1007/978-3-031-22944-2_7

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