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

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arxiv 2101.10918 v1 pith:TSZH3CVQ submitted 2021-01-26 math.CO

Jonathan Turner , Ilias Kotsireas , Dursun Bulutoglu , Andrew Geyer This is my paper · ORCID
classification math.CO
keywords legendrelengthbinarycomplementaryfirstfixedmatricespair
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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 $77$, as well as the first exhaustive generation of Legendre pairs of length $55$.

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  1. Multiplier obstructions for Legendre pairs of length 333

    math.CO 2026-07 accept novelty 7.0 of 10

    A Legendre pair of length 333 cannot be invariant under any common multiplier subgroup of order at least 9; only subgroups of order at most 6 remain possible.

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