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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

On designs of maximal $ (+1,\,-1)$-matrices of order $ n\equiv 2({\rm mod}\ 4)$. II


Author: C. H. Yang
Journal: Math. Comp. 23 (1969), 201-205
MSC: Primary 65.35
Corrigendum: Math. Comp. 28 (1974), 1183.
Corrigendum: Math. Comp. 28 (1974), 1183-1184.
MathSciNet review: 0239748
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Abstract: Finding maximal $ ( + 1, - 1)$-matrices $ {M_{2m}}$ of order $ 2m$ (with odd $ m$) constructible in the standard form

$\displaystyle \left( {\begin{array}{*{20}{c}} A & B \\ { - {B^T}} & {{A^T}} \\ \end{array} } \right)$

is reduced to the finding of two polynomials $ C(w)$, $ D(w)$(corresponding to the circulant submatrices $ A$, $ B$) satisfying

$\displaystyle \vert C(w)\vert^2 + \vert D(w){\vert^2} = \tfrac{1}{2}(m - 1),$ ($ *$)

, where $ w$ is any primitive $ m$th root of unity. Thus, all $ {M_{2m}}$ constructible by the standard form (see [4]) can be classified by the formula $ \left( * \right)$. Some new matrices $ {M_{2m}}$ for $ m = 25,27,31$, were found by this method.

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DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0239748-1
PII: S 0025-5718(1969)0239748-1
Article copyright: © Copyright 1969 American Mathematical Society