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A158865 Smallest maximal excess attained by an equivalence class of Hadamard matrices of order 4n. 0
0, 8, 20, 36, 56, 80, 108, 140 (list; graph; refs; listen; history; text; internal format)



The excess of a {-1,1} matrix is the sum of its elements. The maximal excess of an equivalence class of Hadamard matrices (cf. A007299) is the largest excess attained by a member of the class. The largest maximal excess of any equivalence class is given by A004118.


Best, M. R. The excess of a Hadamard matrix. Nederl. Akad. Wetensch. Proc. Ser. A {80}=Indag. Math. 39 (1977), no. 5, 357-361.

Brown, Thomas A. and Spencer, Joel H., Minimization of +-1 matrices under line shifts. Colloq. Math. 23 (1971), 165-171, 177 (errata).

R. Craigen and H. Kharaghani, Weaving Hadamard matrices with maximum excess and classes with small excess. J. Combinatorial Designs 12 (2004), 233-255.


Table of n, a(n) for n=0..7.


For bounds on a(n), see A004118.


All equivalence classes in orders 20 and 28 attain the same maximal excess. In order 16, three classes attain maximal excess 64 and two attain maximal excess 56. In order 24, 56 equivalence classes attain maximal excess 112 and four attain maximal excess 108.


Sequence in context: A038522 A267435 A186293 * A139570 A265207 A004118

Adjacent sequences:  A158862 A158863 A158864 * A158866 A158867 A158868




William P. Orrick, Mar 28 2009



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Last modified August 19 14:06 EDT 2017. Contains 290808 sequences.