BOUNDS ON MINORS OF BINARY MATRICES

BOUNDS ON MINORS OF BINARY MATRICES

We prove an upper bound on sums of squares of minors of $\{+1, -1\}$-matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin [‘$(1,-1)$-matrices with near-extremal properties’, SIAM J. Discrete Math.23(2009), 1422–1440], but our proof is simpler. We give several corol...

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2013-10, Vol.88 (2), p.280-285
Hauptverfasser: BRENT, RICHARD P., OSBORN, JUDY-ANNE H.
Format: Artikel
Sprache:eng
Schlagworte:
Upper bounds
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Zusammenfassung:We prove an upper bound on sums of squares of minors of $\{+1, -1\}$-matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin [‘$(1,-1)$-matrices with near-extremal properties’, SIAM J. Discrete Math.23(2009), 1422–1440], but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices.
ISSN:0004-9727
1755-1633
DOI:10.1017/S000497271200086X