An Infinite Family of Skew Hadamard Matrices

It has been conjectured that iϊ-matrices and even skew iJ-matrices always exist for n divisible by 4. Constructions of both types of matrices have been given for particular values of n and also for various infinite classes of values (see [1] for the pertinent references). In [1] D. Blatt and G. Szekeres constructed for the first time a skew ίf-matrix of order 52. Their construction is summarized in Theorems 1 and 2 of this paper. Given an additive abelian group G of order 2m + 1, two subsets A c G , BczG, each of order m, are called complementary difference sets in G if ( i ) a G A ==> —a g A, and (ii) for each de (?, d Φ 0, the total number of solutions (αx, α2) e A x A, (&!, b2) e B x B of the equations