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Few-weight quaternary codes via simplicial complexes

  • Received: 18 January 2021 Accepted: 03 March 2021 Published: 10 March 2021
  • MSC : 94B05

  • In this paper, we construct quaternary linear codes via simplicial complexes and we also determine the weight distributions of these codes. Moreover, we present an infinite family of minimal quaternary linear codes, which also meet the Griesmer bound.

    Citation: Xiaomeng Zhu, Yangjiang Wei. Few-weight quaternary codes via simplicial complexes[J]. AIMS Mathematics, 2021, 6(5): 5124-5132. doi: 10.3934/math.2021303

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  • In this paper, we construct quaternary linear codes via simplicial complexes and we also determine the weight distributions of these codes. Moreover, we present an infinite family of minimal quaternary linear codes, which also meet the Griesmer bound.



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    [1] A. Ashikhmin, A. Barg, Minimal vectors in linear codes, IEEE T. Inform. Theory, 44 (1998), 2010-2017. doi: 10.1109/18.705584
    [2] S. Chang, J. Y. Hyun, Linear codes from simplicial complexes, Des. Codes Cryptogr., 86 (2018), 2167-2181. doi: 10.1007/s10623-017-0442-5
    [3] C. Ding, Linear codes from some 2-designs, IEEE T. Inform. Theory, 61 (2015), 3265-3275. doi: 10.1109/TIT.2015.2420118
    [4] M. Grassl, Bounds on the minimum distance of linear codes. Available from: http://www.codetables.de.
    [5] J. H. Griesmer, A bound for error correcting codes, IBM J. Res. Dev., 4 (1960), 532-542. doi: 10.1147/rd.45.0532
    [6] Z. Heng, Q. Yue, A class of binary linear codes with at most three weights, IEEE Commun. Lett., 19 (2015), 1488-1491. doi: 10.1109/LCOMM.2015.2455032
    [7] W. C. Huffman, V. Pless, Fundamentals of error-correcting codes, Cambridge: Cambridge University Press, 2003.
    [8] J. Y. Hyun, H. K. Kim, Y. S. Wu, Q. Yue, Optimal minimal linear codes from posets, Des. Codes Cryptogr., 88 (2020), 2475-2492. doi: 10.1007/s10623-020-00793-0
    [9] J. Y. Hyun, J. Lee, Y. Lee, Infinite families of optimal linear codes constructed from simplicial complexes, IEEE T. Inform. Theory, 66 (2020), 6762-6775. doi: 10.1109/TIT.2020.2993179
    [10] C. J. Li, Q. Yue, F. W. Li, Weight distributions of cyclic codes with respect to pairwise coprime order elements, Finite Fields Th Appl., 28 (2014), 94-114. doi: 10.1016/j.ffa.2014.01.009
    [11] Y. S. Wu, J. Y. Hyun, Few-weight codes over $\Bbb F_p + u\Bbb F_p$ associated with down sets and their distance optimal Gray image, Discrete Appl. Math., 283 (2020), 315-322. doi: 10.1016/j.dam.2020.01.019
    [12] Y. S. Wu, X. M. Zhu, Q. Yue, Optimal few-weight codes from simplicial complexes, IEEE T. Inform. Theory, 66 (2020), 3657-3663. doi: 10.1109/TIT.2019.2946840
    [13] Z. Zhou, X. Li, C. Tang, Binary LCD codes and self-orthogonal codes from a generic construction, IEEE T. Inform. Theory, 65 (2019), 16-27. doi: 10.1109/TIT.2018.2823704
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  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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