A practical algorithm for completing half-Hadamard matrices using LLL

DOI10.1007/s10801-021-01077-zzbMath1484.05032OpenAlexW3212678104MaRDI QIDQ2114786

Yossi Strassler, Assaf Goldberger

Publication date: 15 March 2022

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10801-021-01077-z

zbMATH Keywords

Hadamard matriceslattice basis reductionGram factorization problem

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Proceedings, conferences, collections, etc. pertaining to number theory (11-06) Matrices of integers (15B36)

Uses Software

• SageMath
• Hadamard

Cites Work

• Counting results for thin Butson matrices
• A Fourier-analytic approach to counting partial Hadamard matrices
• The LLL algorithm. Survey and applications
• Integral and rational completions of combinatorial matrices
• Factoring polynomials with rational coefficients
• Conjectures about Hadamard matrices
• Lattice basis reduction: Improved practical algorithms and solving subset sum problems
• A new polynomial-time variant of LLL with deep insertions for decreasing the squared-sum of Gram-Schmidt lengths
• A counterexample to Beder's conjectures about Hadamard matrices
• Generating binary partial Hadamard matrices
• Circulant partial Hadamard matrices
• An LLL Algorithm with Quadratic Complexity
• Predicting Lattice Reduction
• An existence theorem for latin squares
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