Work

Multiplier obstructions for Legendre pairs of length 333

Year: 2026

Type: software

Abstract: Proof-carrying exclusions for multiplier-invariant Legendre pairs of length 333, a structured route to a real Hadamard matrix of order 668. The release analytically excludes the final order-9 multiplier family, proves every common multiplier subgroup of order at least 9 impossible, and closes 21 of 30 mod-3-compatible families. It includes checked DRAT traces or direct pseudo-Boolean certificates, independent verifiers, fixed-field compression refinements, and a reconstruction of the known 64-modular order-668 matrix. This record does not construct or disprove a real Hadamard matrix of order 668; the unrestricted problem remains open.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.21498697

Author: Ramos, Arthur

Institution: Microsoft (United States)

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7170084091

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