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 | References | Similar Articles | Additional Information

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.

- Hartmut Ehlich,
*DeterminantenabschĂ¤tzungen fĂĽr binĂ¤re Matrizen*, Math. Z.**83**(1964), 123â€“132 (German). MR**160792**, DOI https://doi.org/10.1007/BF01111249 - C. H. Yang,
*Some designs for maximal $(+1,\,-1)$-determinant of order $n\equiv 2\,({\rm mod}\,4)$*, Math. Comp.**20**(1966), 147â€“148. MR**188093**, DOI https://doi.org/10.1090/S0025-5718-1966-0188093-9 - C. H. Yang,
*A construction for maximal $(+1,\,-1)$-matrix of order $54$*, Bull. Amer. Math. Soc.**72**(1966), 293. MR**188239**, DOI https://doi.org/10.1090/S0002-9904-1966-11497-0 - C. H. Yang,
*On designs of maximal $(+1,\,-1)$-matrices of order $n\equiv 2({\rm mod}\ 4)$*, Math. Comp.**22**(1968), 174â€“180. MR**225476**, DOI https://doi.org/10.1090/S0025-5718-1968-0225476-4 - John Williamson,
*Hadamardâ€™s determinant theorem and the sum of four squares*, Duke Math. J.**11**(1944), 65â€“81. MR**9590**

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Article copyright:
© Copyright 1969
American Mathematical Society