Infinite families of 3-designs from a type of five-weight code
Infinite families of 3-designs from a type of five-weight code
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DOI：
10.1007/s10623-017-0352-6
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
C. Ding
中科院分区：
文献类型：
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作者：
C. Ding
长期以来，人们已经知道，设计可以用来构造线性和非线性码，并且码中具有固定重量的码字可以保持在设计时。虽然在从试验设计构造规范的方向上已经取得了很大的进展，但从规范构造试验设计的工作却很少。本文的目的是从一类五权二元线性码中构造2-设计和3-设计的无限族。本文所得到的2-设计和3-设计的总数在任何奇数处都是指数分布的，并且设计的区组大小变化范围很大。
It has been known for a long time thatt-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold at-design. While a lot of progress in the direction of constructing codes fromt-designs has been made, only a small amount of work on the construction oft-designs from codes has been done. The objective of this paper is to construct infinite families of 2-designs and 3-designs from a type of binary linear codes with five weights. The total number of 2-designs and 3-designs obtained in this paper are exponential in any oddmand the block size of the designs varies in a huge range.