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Complete weight enumerators of some linear codes from quadratic forms

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Abstract

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of q-ary linear codes with few weights employing general quadratic forms over the finite field \({\mathbb {F}}_{q}\) is proposed, where q is an odd prime power. This generalizes some earlier constructions of p-ary linear codes from quadratic bent functions over the prime field \({\mathbb {F}}_{p}\), where p is an odd prime. The complete weight enumerators of the resultant q-ary linear codes are also determined.

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Acknowledgments

The authors are very grateful to the reviewers and the Editor, Prof. Cunsheng Ding, for their valuable comments that improved the presentation of this paper. This work was supported in part by the National Science Foundation of China under Grant 11571285 and the Sichuan Provincial Youth Science and Technology Fund under Grant 2016JQ0004.

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Authors and Affiliations

  1. The Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, 610031, China

    Dan Zhang, Daiyuan Peng & Xiaohu Tang

  2. Science and Technology on Communication Security Laboratory, Maibox 810, 610041, Chengdu, Sichuan, China

    Dan Zhang & Xiaohu Tang

  3. School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, 610031, China

    Cuiling Fan

  4. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Cuiling Fan

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  1. Dan Zhang
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  2. Cuiling Fan
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  3. Daiyuan Peng
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  4. Xiaohu Tang
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Correspondence to Cuiling Fan.

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Zhang, D., Fan, C., Peng, D. et al. Complete weight enumerators of some linear codes from quadratic forms. Cryptogr. Commun. 9, 151–163 (2017). https://doi.org/10.1007/s12095-016-0190-9

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  • DOI: https://doi.org/10.1007/s12095-016-0190-9

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