In this paper, a new construction method for synthesizing two- and hig
her-dimensional quadratic residue arrays is introduced. The constructi
on is mainly based on addressing the elements of an m-dimensional arra
y by the elements of Galois Field GF(p(m)), where p denotes an odd pri
me and m denotes an integer. With a following mapping, the elements of
the m-dimensional array, except the leading element, are set to eithe
r + 1 or - 1. The dimensions of the resulting m-dimensional arrays hav
e the size p. It is shown that the periodic autocorrelation function o
f these quadratic residue arrays are two- or three-level, depending on
whether the number of elements is N = 1 mod 4 or N = 3 mod 4. With th
ese quadratic residue arrays, new classes of two- and higher-dimension
al pseudonoise and Legendre arrays are obtained.