On designs of maximal matrices of order . II
Author:
C. H. Yang
Journal:
Math. Comp. 23 (1969), 201205
MSC:
Primary 65.35
Corrigendum:
Math. Comp. 28 (1974), 1183.
Corrigendum:
Math. Comp. 28 (1974), 11831184.
MathSciNet review:
0239748
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Abstract: Finding maximal matrices of order (with odd ) constructible in the standard form is reduced to the finding of two polynomials , (corresponding to the circulant submatrices , ) satisfying  ()  , where is any primitive th root of unity. Thus, all constructible by the standard form (see [4]) can be classified by the formula . Some new matrices for , were found by this method.
 [1]
Hartmut
Ehlich, Determinantenabschätzungen für binäre
Matrizen, Math. Z. 83 (1964), 123–132 (German).
MR
0160792 (28 #4003)
 [2]
C.
H. Yang, Some designs for maximal
(+1,1)determinant of order
𝑛≡2(𝑚𝑜𝑑4), Math. Comp. 20 (1966), 147–148. MR 0188093
(32 #5534), http://dx.doi.org/10.1090/S00255718196601880939
 [3]
C.
H. Yang, A construction for maximal
(+1,1)matrix of order 54, Bull. Amer. Math.
Soc. 72 (1966), 293.
MR
0188239 (32 #5678), http://dx.doi.org/10.1090/S000299041966114970
 [4]
C.
H. Yang, On designs of maximal (+1,1)matrices
of order 𝑛≡2(𝑚𝑜𝑑\4), Math. Comp. 22 (1968), 174–180. MR 0225476
(37 #1069), http://dx.doi.org/10.1090/S00255718196802254764
 [5]
John
Williamson, Hadamard’s determinant theorem and the sum of
four squares, Duke Math. J. 11 (1944), 65–81.
MR
0009590 (5,169g)
 [1]
 H. Ehlich, ``Determinantenabschätzungen für binäre Matrizen,'' Math. Z., v. 83, 1964, pp. 123132. MR 0160792 (28:4003)
 [2]
 C. H. Yang, ``Some designs for maximal determinant of order ,'' Math. Comp., v. 20, 1966, pp. 147148. MR 32 #5534. MR 0188093 (32:5534)
 [3]
 C. H. Yang, ``A construction for maximal matrix of order 54,'' Bull. Amer. Math. Soc., v. 72, 1966, p. 293. MR 32 #5678. MR 0188239 (32:5678)
 [4]
 C. H. Yang, ``On designs of maximal matrices of order ,'' Math. Comp., v. 22, 1968, pp. 174180. MR 0225476 (37:1069)
 [5]
 J. Williamson, ``Hadamard's determinant theorem and the sum of four squares,'' Duke Math. J., v. 11, 1944, pp. 6581. MR 5, 169. MR 0009590 (5:169g)
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DOI:
http://dx.doi.org/10.1090/S00255718196902397481
PII:
S 00255718(1969)02397481
Article copyright:
© Copyright 1969
American Mathematical Society
