2013/11/28 by Víctor Álvarez, Álvarez, V., José Ándrés Armario +5
Computer Science · Engineering · Mathematics · #05B20 #15A15 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1311.7250
openalex publication_date 2013/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An n by n skew-symmetric type (-1,1)-matrix K=[ki,j] has 1's on the main diagonal and ± 1's elsewhere with ki,j=-kj,i. The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n≡ 0 \mod 4 (skew-Hadamard matrices), but for n≡ 2\mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (-1,1)-matrices of skew type. Some explicit calculations have been done up to t=11. To our knowledge, the upper bounds on the maximal determinant in orders 18 and 22 have been improved.