English

Legendre pair of length $77$ using complementary binary matrices with fixed marginals

Combinatorics 2021-01-27 v1

Abstract

We provide a search method for Legendre pairs of composite length based on generating binary matrices with fixed row and column sums from compressed, complementary integer vectors. This approach yielded the first construction of a Legendre pair of length 7777, as well as the first exhaustive generation of Legendre pairs of length 5555.

Cite

@article{arxiv.2101.10918,
  title  = {Legendre pair of length $77$ using complementary binary matrices with fixed marginals},
  author = {Jonathan Turner and Ilias Kotsireas and Dursun Bulutoglu and Andrew Geyer},
  journal= {arXiv preprint arXiv:2101.10918},
  year   = {2021}
}

Comments

17 pages, 1 figure. Submitted to Designs, Codes and Cryptography

R2 v1 2026-06-23T22:33:11.255Z