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Optimal Multiply Constant-weight Codes from Generalized Howell Designs

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Abstract

Constructions for optimal multiply constant-weight codes (MCWCs) with total weight 5 and distance 8 are studied. The equivalence between a special class of MCWCs and generalized Howell designs (GHDs) is established. The existences of GHD\(\big (\frac{3n-3}{2},3n\big )\)s and GHD\(\big (\frac{3n-5}{2},3n\big )\)s are discussed. As corollaries, a large number of optimal MCWCs are obtained.

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Authors and Affiliations

  1. Institute of Mathematics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Changyuan Wang, Yanxun Chang & Tao Feng

  2. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, People’s Republic of China

    Changyuan Wang

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  1. Changyuan Wang
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  2. Yanxun Chang
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  3. Tao Feng
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Correspondence to Tao Feng.

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Supported by NSFC under Grant 11431003, 11471032, and Fundamental Research Funds for the Central Universities under Grant 2016JBM071, 2016JBZ012.

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Wang, C., Chang, Y. & Feng, T. Optimal Multiply Constant-weight Codes from Generalized Howell Designs. Graphs and Combinatorics 35, 611–632 (2019). https://doi.org/10.1007/s00373-019-02020-7

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