Legendre pair of length $77$ using complementary binary matrices with fixed marginals
Jonathan Turner, Ilias Kotsireas, Dursun Bulutoglu, Andrew Geyer
TL;DR
This paper introduces a novel search method for constructing Legendre pairs of composite lengths using binary matrices with fixed marginals, successfully generating pairs of lengths 77 and 55 for the first time.
Contribution
The paper presents a new approach to generate Legendre pairs of composite lengths through compressed binary matrices, leading to the first known pair of length 77 and exhaustive generation of length 55.
Findings
First construction of Legendre pair of length 77
Exhaustive generation of Legendre pairs of length 55
New binary matrix-based search method
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 , as well as the first exhaustive generation of Legendre pairs of length .
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