2014/01/09 by Jingjun Bao, Bao, Jingjun, Lijun Ji +1
Engineering · Mathematics · #05B30 #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Optimization and Packing Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1401.2022
openalex publication_date 2014/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 3-(n,4,1) packing design consists of an n-element set X and a collection of 4-element subsets of X, called \it 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 undecided 21 packing numbers A(n,4,4) are shown to be equal to Johnson bound J(n,4,4) ( =\lfloor(n)/(4)\lfloor(n-1)/(3)\lfloor(n-2)/(2)\rfloor\rfloor\rfloor) where n=6k+5, k∈ \m: m is odd, 3≤ m≤ 35, m≠ 17,21\∪ \45,47,75,77,79,159\.