T-Wise Balanced Designs from Binary Hamming Codes

Abstract

In this paper we show that the binary Hamming codes $(2^r-1, 2^{2^r-r-1}-2, 3)$ satisfy $(2^r-r-2) -2^{2^r-r-1}-1, \{3,4,...,2^r-4\}, 1)$ designs, 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.