Array Correlation and Sequences with Equal Magnitude Correlation

Abstract

In this paper, we will investigate cross correlation of sequences over ℝ where ℝ is either the integer residue ring ℤ q or the Galios ring G(p e , d) where q, e and d are positive integers and p is a prime. First, in terms of the interleaved structure of sequences, we will introduce a new type of cross correlation between two periodic sequences over ℝ with period v = nm where n > 1 and m > 1 are positive integers, which will be called an array cross/auto correlation in this paper. Then, we will construct two families of sequences over ℝ of period v = nm. We will show that for each pair of sequences, each taken from different sets, their cross correlation (as a usual definition) is equal to their array cross correlation. Moreover, the magnitude of the sum of each correlation value and the constant 1 is equal to the constant n − 1.