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Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications

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Abstract

Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an odd prime p, the complete weight enumerator of a class of p-ary linear codes based on defining sets are determined. Furthermore, from the explicit complete weight enumerator of linear codes, a new class of optimal constant composition codes and several classes of asymptotically optimal systematic authentication codes are obtained.

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Authors and Affiliations

  1. Institute of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China

    Qunying Liao

  2. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518061, China

    Xiaofeng Wang

Authors
  1. Haibo Liu
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  2. Qunying Liao
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  3. Xiaofeng Wang
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Corresponding author

Correspondence to Qunying Liao.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11401408, Project of Science and Technology Department of Sichuan Province under Grant No. 2016JY0134, the National Key R and Program of China under Grant No. 2016QY04W080

This paper was recommended for publication by Editor ZHANG Zhifang.

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Liu, H., Liao, Q. & Wang, X. Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications. J Syst Sci Complex 32, 947–969 (2019). https://doi.org/10.1007/s11424-018-7414-3

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  • DOI: https://doi.org/10.1007/s11424-018-7414-3

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