Title :
A New Family of
-Ary Sequences of Period
With Low Correlation
Author :
Kim, Ji-Youp ; Choi, Sung-Tai ; No, Jong-Seon ; Chung, Habong
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Seoul Nat. Univ., Seoul, South Korea
fDate :
6/1/2011 12:00:00 AM
Abstract :
For an odd prime p congruent to 3 modulo 4 and an odd integer n, a new family of p-ary sequences of period N=(pn-1)/2 with low correlation is proposed. The family is constructed by shifts and additions of two decimated m-sequences with the decimation factors 2 and 2d, d = N - pn-1. The upper bound for the maximum magnitude of nontrivial correlations of this family is derived using well known Kloosterman sums. The upper bound is shown to be 2√(N+1/2) = √(2pn) , which is twice the Welch´s lower bound and approximately 1.5 times the Sidelnikov´s lower bound. The size of the family is 2(pn-1) , which is four times the period of sequences.
Keywords :
correlation methods; number theory; sequences; Kloosterman sums; Sidelnikov lower bound; Welch lower bound; decimation factor; low correlation; maximum magnitude; nontrivial correlation; odd integer; odd prime; p-ary sequence; Additives; Arrays; Correlation; Electrical engineering; Gold; Upper bound; Autocorrelation; Kloosterman sums; characters; cross-correlation; finite fields; nonbinary sequences;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2133730