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


Author: C. H. Yang
Journal: Math. Comp. 23 (1969), 201-205
MSC: Primary 65.35
DOI: https://doi.org/10.1090/S0025-5718-1969-0239748-1
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 \[ \left ( {\begin {array}{*{20}{c}} A & B \\ { - {B^T}} & {{A^T}} \\ \end {array} } \right )\] is reduced to the finding of two polynomials $C(w)$, $D(w)$(corresponding to the circulant submatrices $A$, $B$) satisfying \begin{equation}\tag {$*$} |C(w)|^2 + |D(w){|^2} = \tfrac {1}{2}(m - 1),\end{equation} , 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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Article copyright: © Copyright 1969 American Mathematical Society