Two Classes of Large Families of Sequences with low Correlation
Fanxin Zeng Β· 2007
In this paper, two classes of large families of sequences of length ππ-1 is proposed, where π is a prime number, π is an even number, π = 2π. One of them is binary, the new sequences have large family size 22πand seven-valued correlations, {-2π-1,-1,2π-1,2Β·2π-1,3Β·2π-1,4Β·2π-1,5Β·2π-1}. The other is binary or ployphase, depending upon choice of the parameter π, the new sequences possess the large family size π(πΉ-1)π, and at most 2πΉ correlation levels, {-ππ-1, -1,ππ-1,2ππ-1,Β·Β·Β·,(2πΉ-2)ππ-1}, where πΉ is a positive integer such that πΉ β₯ 2.In addition, the later one includes the sequences with Niho-type decimations,2ππ-1(called as Niho sequences for π = 2 and Helleseth sequences for π > 2,respectively) and 3 Β· 2π-2, as special cases.