A note on the nonexistence of Barker sequences

✍ Scribed by Jonathan Jedwab; Sheelagh Lloyd

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 247 KB
• Volume: 2
• Category: Article
• ISSN: 0925-1022
• DOI: 10.1007/bf00124212

✦ Synopsis

A Barker sequence is a sequence with elements +1 such that all out-of-phase aperiodic autocorrelation coefficients are 0, 1 or -1. It is known that ifa Barker sequence of length s > 13 exists then s = 4N 2 for some odd integer N _> 55, and it has long been conjectured that no such sequence exists. We review some previous attempts to improve the bound on N which, unfortunately, contain errors. We show that a recent theorem of Eliahou et al. [5] rules out all but six values of N less than 5000, the smallest of which is 689.