Combinatorial Hermitian algebras derived from Latin squares

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