A new family of supplementary difference sets and Hadamard matrices
The authors [J. Comb. Theory, Ser. A 58, No. 2, 310-317 (1991; Zbl 0758.05032)] showed that for any prime power \(q\equiv 1\pmod 4\) there exist \(4\)-\(\{v; k, k, k, k; \lambda\}\) supplementary difference sets with \(v= q^2\), \(k= q(q- 1)/2\), \(\lambda= 4k- v\) (difference sets \(D_1\), \(D_2\), \(D_3\), \(D_4\) are called \(4\)-\(\{v; k, k, k, k; \lambda\}\) supplementary if their elements are residues \(\text{mod } v\) and their parameters are of the form \((v, k, \lambda)\)). In this paper, the same authors prove that there exist \(4\)-\(\{v; k, k, k, k; \lambda\}\) supplementary difference sets with \(v= q^2\), \(q\equiv 3\pmod 8\) a prime power, \(k= q(q- 1)/2\), \(\lambda= 4k- v\) and Hadamard matrices of order \(4v\).
scientific article; zbMATH DE number 906667