Legendre Pair of Length 77 Using Complementary Binary Matrices with Fixed Marginals
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 77, as well as the first exhaustive generation of Legendre pairs of length 55.
Designs, Codes and Cryptography
Turner, J. S., Kotsireas, I., Bulutoglu, D. A., & Geyer, A. (2021). Legendre pair of length $77$ using complementary binary matrices with fixed marginals. Designs, Codes and Cryptography, 89, 1321–1333. https://doi.org/10.1007/s10623-021-00862-y; Sourced from http://arxiv.org/abs/2101.10918