最优常重覆盖码
Optimal Constant Weight Covering Codes
令 表示 上长度为n重量为w的码字个数最小值，使得任意一个重量为t的字与其中至少一个码字间的汉明距离不大于d。本文确定了当n≥4，q=3,4 或 q= +1(m≥2)时，除了(q,n)=(3,5)以外，所有 的值。我们的构造方法主要是基于一类名为H-frame的辅助设计，这类设计在可分组3BD的循环构造中起到了类似于烛台型设计在3平衡设计构造中的重要作用。
Let be the minimum size of a code over of length n, constant weight w, such that every word with weight t is within Hamming distance d of at least one codeword. In this paper, we determine for all n≥4, q=3, 4 or q= +1 with m≥2, leaving the only case (q,n)=(3,5) in doubt. Our construction method is mainly based on the auxiliary designs, H-frames, which play a crucial role in the recursive constructions of group divisible 3-designs similar to that of candelabra systems in the constructions of 3-wise balanced designs.
张先得、葛根年、张会
数学
组合数学常重覆盖码可分组t-覆盖可分组t-设计H-frame
ombinatoricsConstant weight covering codesgroup divisible t-coveringgroup divisible t-designH-frame
张先得,葛根年,张会.最优常重覆盖码[EB/OL].(2010-10-26)[2025-08-16].http://www.paper.edu.cn/releasepaper/content/201010-486.点此复制
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