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A family of projective two-weight linear codes

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Abstract

Projective two-weight linear codes are closely related to finite projective spaces and strongly regular graphs. In this paper, a family of q-ary two-weight linear codes including two subfamilies of projective codes is presented, where q is a prime power. The parameters of both the codes and their duals are excellent. As applications, the codes are used to derive strongly regular graphs with new parameters and secret sharing schemes with interesting access structures.

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Authors and Affiliations

  1. School of Science, Chang’an University, Xi’an, 710064, China

    Ziling Heng, Dexiang Li & Fuling Chen

  2. School of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Jiao Du

  3. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Xinxiang, 453007, China

    Jiao Du

Authors
  1. Ziling Heng
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  2. Dexiang Li
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  3. Jiao Du
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  4. Fuling Chen
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Correspondence to Ziling Heng.

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Communicated by T. Helleseth.

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The research of Z. Heng was supported in part by the National Natural Science Foundation of China under Grant 11901049, in part by the the Natural Science Basic Research Program of Shaanxi under Grant 2020JQ-343, and in part by the Young Talent Fund of University Association for Science and Technology in Shaanxi, China, under Grant 20200505. The research of J. Du was supported by the National Natural Science Foundation of China under Grant 11971004.

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Heng, Z., Li, D., Du, J. et al. A family of projective two-weight linear codes. Des. Codes Cryptogr. 89, 1993–2007 (2021). https://doi.org/10.1007/s10623-021-00896-2

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  • DOI: https://doi.org/10.1007/s10623-021-00896-2

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