@inproceedings{Borwein2013WieferichPA,
title={Wieferich Pairs and Barker Sequences , Ii},
author={Peter Borwein and Michael J. Mossinghoff},
year={2013}
}

We show that if a Barker sequence of length n > 13 exists, then either n = 3 979 201 339 721 749 133 016 171 583 224 100, or n > 4 · 1033. This improves the lower bound on the length of a long Barker sequence by a factor of nearly 2000. We also obtain 18 additional integers n < 1050 that cannot be ruled out as the length of a Barker sequence, and find more than 237000 additional candidates n < 10100, the vast majority of which appear likely to satisfy all of the known restrictions on the length… CONTINUE READING