Two Classes of Large Families of Sequences with low Correlation

Abstract

In this paper, two classes of large families of sequences of length pⁿ-1 is proposed, where p is a prime number, n is an even number, n = 2m. One of them is binary, the new sequences have large family size 2²ⁿ and seven-valued correlations, {-2^m-1,-1,2^m-1,2ldr2^m-1,3ldr2^m-1,4ldr2^m -1,5 ldr2^m -1}. The other is binary or ployphase, depending upon choice of the parameter p, the new sequences possess the large family size p(d-1)n, and at most 2d correlation levels, {-p^m -1, -1,p^m -1,2p^m -1, ldrldrldr , (2d -2)p^m -1}, where d is a positive integer such that d ges 2.1n addition, the later one includes the sequences with Niho-type decimations,2p^m-1(called as Niho sequences for p = 2 and Helleseth sequences for p > 2,respectively) and 3 ldr2^m-2, as special cases.