The existence of a Bush-type Hadamard matrix of order 36 and two new infinite classes of symmetric designs

摘要

A nonsymmetric Bush-type Hadamard matrix of order 36 is constructed which leads to two, new infinite classes of symmetric designs with parameters: v = 36(25(m) + 25(m-1) + ... + 25 + 1), k = 15(25)(m), lambda = 6(25)(m), and v = 36(49(m) + 49(m-1) + ... + 49 + 1), k = 21(49)(m), lambda = (49)(m), where ni is any positive integer. (C) 2001 Academic Press. [References: 6]