Combinatorial Hermitian algebras derived from Latin squares

Abstract

This paper presents an infinite class of algebras of Hermitian matrices of size ( 4 n + 1 ) × ( 4 n + 1 ) , where n is a positive integer and where ( 4 n + 1 ) is a prime number or a power of a prime number (so that the Galois Field GF ( 4 n + 1 ) exists). For each such n, we obtain 4 n separate Hermitian algebras, no two of which mutually commute.