Representations by Hermitian Forms in a Finite Field of Characteristic Two

Abstract

Throughout this paper, we let q = 2W,﹜ w a positive integer, and for u = 1 or 2, we let GF(qu) denote the finite field of cardinality qu. Let - denote the involutory field automorphism of GF(q2) with GF(q) as fixed subfield, where ā = aQ for all a in GF﹛q2). Moreover, let | | denote the norm (multiplicative group homomorphism) mapping of GF(q2) onto GF(q), where |a| — a • ā = aQ+1.