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The completion of optimal cyclic quaternary codes of weight 3 and distance 3

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Abstract

A cyclic \((n,d,w)_q\) code is a cyclic q-ary code of length n, constant weight w and Hamming distance at least d. The function \(CA_{q}(n,d,w)\) denotes the largest possible size of a cyclic \((n,d,w)_q\) code. A new construction, which is based on two (n, 2, 1) cyclic difference packings with given properties, is proposed for optimal \((n, 3, 3)_4\) codes. As a result, the exact value of \(CA_{4}(n,3,3)\) is determined for \(n \equiv 18\pmod {24}\), and the spectrum of \(CA_{4}(n,3,3)\) is then completely determined.

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Acknowledgements

The authors would like to thank the Editor and the anonymous reviewers for their helpful comments, which has significantly improved the presentation of our manuscript. Supported by NSFC under Grant 11971053 (Y. Chang), NSFC under Grant 11901210 and China Postdoctoral Science Foundation under Grant 2019M652924 (L. Lan), NSFC under Grant 11771119 and NSFHB under Grant A2019507002 (L. Wang).

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Authors and Affiliations

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, People’s Republic of China

    Liantao Lan

  2. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Yanxun Chang

  3. School of Intelligence Policing, China People’s Police University, Langfang, 065000, People’s Republic of China

    Lidong Wang

  4. School of Computer Science, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Liantao Lan

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  1. Liantao Lan
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  2. Yanxun Chang
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  3. Lidong Wang
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Correspondence to Yanxun Chang.

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Communicated by M. Buratti.

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Lan, L., Chang, Y. & Wang, L. The completion of optimal cyclic quaternary codes of weight 3 and distance 3. Des. Codes Cryptogr. 90, 851–862 (2022). https://doi.org/10.1007/s10623-022-01006-6

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  • DOI: https://doi.org/10.1007/s10623-022-01006-6

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