A FOURIER TRANSFORM APPROACH FOR IMPROVING THE LEVENSHTEIN'S LOWER BOUND ON APERIODIC CORRELATION OF BINARY SEQUENCES

作者：Yu Nam Yul^*

来源：Advances in Mathematics of Communications, 2014, 8(2): 209-222.

DOI：10.3934/amc.2014.8.209

• Aperiodic correlation
• binary sequences
• Levenshtein bound
• Welch bound

A binary sequence family S of length n and size M can be characterized by the maximum magnitude of its nontrivial aperiodic correlation, denoted as theta(max)(S). The lower bound on theta(max)(S) was originally presented by Welch, and improved later by Levenshtein. In this paper, a Fourier transform approach is introduced in an attempt to improve the Levenshtein's lower bound. Through the approach, a new expression of the Levenshtein bound is developed. Along with numerical supports, it is found that theta(2)(max)(S) > 0.3584n - 0.0810 for M = 3 and n >= 4, and theta(2)(max)(S) > 0.4401n - 0.1053 for M = 4 and n >= 4, respectively, which are tighter than the original Welch and Levenshtein bounds.

• 出版日期2014-5