Wieferich Prime Pairs, Barker Sequences, and Circulant Hadamard Matrices

Michael Mossinghoff

This page contains data associated with two articles.

  1. Double Wieferich pairs and circulant Hadamard matrices, by B. Logan and M. J. Mossinghoff.
  2. Wieferich pairs and Barker sequences, II, by P. Borwein and M. J. Mossinghoff, LMS J. Comput. Math. 17 (2014), no. 1, 24-32.
It includes lists of Wieferich prime pairs associated with computations performed for these articles, and integers n that have not been eliminated as the order of a large circulant Hadamard matrix, and integers that have not been eliminated as the possible length of a long Barker sequence.

Recall that a Wieferich prime pair (q, p) has the property that qp−1 = 1 mod p2. A circulant Hadamard matrix of order n is an n × n matrix of ±1's whose rows are mutually orthogonal, and each of whose rows after the first is obtained from the prior one by cyclically shifting its elements by one position to the right. A Barker sequence is a finite sequence {ai}, each term ±1, for which each sum of the form ∑i aiai+k with k ≠ 0 is −1, 0, or 1.

Circulant Hadamard Matrices

Barker Sequences

Related Links

Michael Mossinghoff
mimossinghoff at davidson dot edu

Last modified August 2, 2015.