English

Barker sequences of odd length

Combinatorics 2015-01-27 v1 Information Theory math.IT

Abstract

A Barker sequence is a binary sequence for which all nontrivial aperiodic autocorrelations are at most 1 in magnitude. An old conjecture due to Turyn asserts that there is no Barker sequence of length greater than 13. In 1961, Turyn and Storer gave an elementary, though somewhat complicated, proof that this conjecture holds for odd lengths. We give a new and simpler proof of this result.

Keywords

Cite

@article{arxiv.1501.06035,
  title  = {Barker sequences of odd length},
  author = {Kai-Uwe Schmidt and Jürgen Willms},
  journal= {arXiv preprint arXiv:1501.06035},
  year   = {2015}
}

Comments

6 pages, this note supersedes the main result of arXiv:1409.1434

R2 v1 2026-06-22T08:12:02.113Z