A new weight vector for a tighter levenshtein bound on aperiodic correlation

Abstract

The Levenshtein bound on aperiodic correlation, which is a function of the weight vector,is tighter than the Welch bound for sequence sets over the complex roots of unity when M 4 and 2 where M denotes the set size and n the sequence length. Although it is known that the tightest Levenshtein bound is equal to the Welch bound for Min{1,2}it is unknown whether the Levenshtein bound can be tightened for M=3,and Levenshtein,in his paper published in 1999,postulated that the answer may be negative.A new weight vector is proposed in this paper, which leads to a tighter Levenshtein bound for M=3 n3 and M 4n 2.In addition,the explicit form of the weight vector (which is derived by relating the quadr..