Linear codes and the existence of a reversible Hadamard difference set in Z(2) x Z(2) x Z(5)(4)

[摘要] Linear codes over GF(5) are utilized for the construction of a reversible abelian Hadamard difference set in Z(2) x Z(2) x Z(5)(4). This is the first trample of an abelian Hadamard difference set in a group of order divisible by a prime p = 1 (mod 4). Applying the Turyn composition theorem, one obtains abelian difference sets and Hadamard matrices of Williamson type of order 4 x 5(4n) x p(1)(4n1) x ... x p(1)(4n1) where n,n(1),...,n(1) are arbitrary non-negative integers and each p(i) is a prime, p(i) = 3 (mod 4). (C) 1997 Academic Press.

[发布日期] 1997-07-01