Asymptotic determination of the last packing number of quadruples

作者：Ji L^*

来源：Designs, Codes and Cryptography, 2006, 38(1): 83-95.

DOI：10.1007/s10623-004-5662-9

• constant weight code
• packing design
• candelabra system
• s-fan design

A 3-(n,4,1) packing design consists of an n-element set X and a collection of 4-element subsets of X, called blocks, such that every 3-element subset of X is contained in at most one block. The packing number of quadruples d(3,4,n) denotes the number of blocks in a maximum 3-(n,4,1) packing design, which is also the maximum number A(n,4,4) of codewords in a code of length n, constant weight 4, and minimum Hamming distance 4. In this paper the last packing number A(n,4,4) for n = 5(mod 6) is shown to be equal to Johnson bound J (n, 4, 4)(= [N/4[N-13[N-2/2]]] with 21 undecided values n = 6k + 5, k is an element of {m : m is odd, 3 <= m <= 35, m not equal 17, 21}.{45, 47, 75, 77, 79, 159}.

• 出版日期2006-1
• 单位苏州大学; 宿州学院