QUADRATIC RESIDUE ARRAYS

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.