A matrix H=[dijβ] is a generalized Hadamard matrix of order uΞ»
with entries from U which is a finite group of order u (for short
GH(u,Ξ»)) such that whenever iξ =β the set
{dijβdβjβ1ββ£1β€jβ€uΞ»} contains each element of
U exactly Ξ» times. In this paper, we construct GH(q,q)'s
and GH(q,q2)'s over additive groups of finite fields
GF(q)'s by using some sorts of functions