Asymptotic Determination of the Last Packing Number of Quadruples |
| |
Authors: | L Ji |
| |
Institution: | (1) Department of Mathematics, Suzhou University, Suzhou, 215006, China |
| |
Abstract: | 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
with 21 undecided values n=6k+5, k∈{m: m is odd , 3≤ m≤ 35, m≠ 17,21}∪ {45,47,75,77,79,159}.
AMS Classification:05B40, 94B25 |
| |
Keywords: | constant weight code packing design candelabra system s-fan design |
本文献已被 SpringerLink 等数据库收录! |
|