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Trace codes over \({\mathbb {Z}}_4,\) and Boolean functions

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Abstract

We construct trace codes over \(\mathbb {Z}_4\) based on Boolean functions and their support. The Lee weight distribution of these codes is studied by using the Walsh–Hadamard transform of the Boolean functions, and exponential character sums. We obtain few weights codes. In particular, bent and semi-bent functions give three-weight codes.

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Acknowledgements

This research is supported by National Natural Science Foundation of China (61672036), Excellent Youth Foundation of Natural Science Foundation of Anhui Province (1808085J20), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (05015133), Key projects of support program for outstanding young talents in Colleges and Universities (gxyqZD2016008) and China Postdoctoral Science Foundation (Grant No. 2016M601991).

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Authors and Affiliations

  1. Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, Anhui University, No.3 Feixi Road, Hefei, 230039, Anhui, China

    Minjia Shi

  2. School of Mathematical Sciences, Anhui University, Hefei, 230601, Anhui, China

    Minjia Shi, Yan Liu & Lin Sok

  3. LTCI/Telecom ParisTech, 46 rue Barrault, 75013, Paris, France

    Hugues Randriam

  4. Department of Mathematics, Royal University of Phnom Penh, Phnom Penh, 12156, Cambodia

    Lin Sok

  5. CNRS/LAGA, University of Paris 8, 2, rue de la Liberté, 93 526, Saint-Denis, France

    Patrick Solé

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  1. Minjia Shi
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  2. Yan Liu
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  3. Hugues Randriam
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  4. Lin Sok
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  5. Patrick Solé
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Correspondence to Lin Sok.

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Communicated by T. Helleseth.

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Shi, M., Liu, Y., Randriam, H. et al. Trace codes over \({\mathbb {Z}}_4,\) and Boolean functions. Des. Codes Cryptogr. 87, 1447–1455 (2019). https://doi.org/10.1007/s10623-018-0542-x

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  • DOI: https://doi.org/10.1007/s10623-018-0542-x

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