T-Wise Balanced Designs from Binary Hamming Codes

Abstract

In \u00a0this \u00a0paper \u00a0we \u00a0show \u00a0that \u00a0the \u00a0binary \u00a0Hamming \u00a0codes $(2^r-1, 2^{2^r-r-1}-2, 3)$\u00a0satisfy\u00a0$(2^r-r-2) -2^{2^r-r-1}-1, \{3,4,...,2^r-4\}, 1)$\u00a0designs, where $r\ge 3,$ a positive integer. For different values of $r$ most of the $t$-wise balanced designs obtained from our constructions appear to be new.