SYMMETRY GROUPS OF SOME HADAMARD MATRICES

Abstract

Hadamard matrices are a special class of square matrices with entries 1 and -1 only. They have many applications in Coding Theory, Physics, Chemistry and Neural networks. Therefore, this paper makes an attempt to study Hadamard matrices and their connection with Group Theory. Especially, we concentrate on the Symmetry groups of Standard Hadamard matrices  and  It is shown that the Symmetry group of the Standard Hadamard matrices  and  is the trivial group and that of  is isomorphic to the Permutation group Since Symmetry group of the Standard Hadamard matrix  is isomorphic to the General linear group of  invertible matrices over the field  and the order of the General linear group  of  invertible matrices over a finite field  containing  elements is , it is shown that the orders of the Symmetry groups of  and  are 168 and 20,160 respectively,