Maximal binary matrices and sum of two squares
Author:
C. H. Yang
Journal:
Math. Comp. 30 (1976), 148153
MSC:
Primary 05B20
MathSciNet review:
0409235
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Abstract: A maximal matrix of order 66 is constructed by a method of matching two finite sequences. This method also produced many new designs for maximal matrices of order 42 and new designs for a family of Hmatrices of order . A nonexistence proof for a type Hmatrix of order 36, consequently for Golay complementary sequences of length 18, is also given.
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S. JAUREGUI, JR., "Complementary sequences of length 26," IRE Trans. Information Theory, v. IT8, 1962, p. 323.
 [1]
 H. EHLICH, "Determinantenabschä'tzungen für binäre Matrizen," Math. Z., v. 83, 1964, pp. 123132. MR 28 #4003. MR 0160792 (28:4003)
 [2]
 J. BRENNER & L. CUMMINGS, "The Hadamard maximum determinant problem," Amer. Math. Monthly, v. 79, 1972, pp. 626630. MR 46 #190. MR 0301030 (46:190)
 [3]
 R. J. TURYN, "Complex Hadamard matrices," in Combinatorial Structures and Their Applications (Proc. Calgary Internat. Conf., Calgary, Alta., 1969), Gordon and Breach, New York, 1970, pp. 435437. MR 42 #5821. MR 0270938 (42:5821)
 [4]
 C. H. YANG, "On designs of maximal matrices of order . II," Math. Comp., v. 23, 1969, pp. 201205. MR 0239748 (39:1105)
 [5]
 C. H. YANG, "On Hadamard matrices constructible by circulant submatrices," Math. Comp., v. 25, 1971, pp. 181186. MR 44 #5235. MR 0288037 (44:5235)
 [6]
 M. J. E. GOLAY, "Complementary series," IRE Trans. Information Theory, v. IT7, 1961, pp. 8287. MR 23 #A3096. MR 0125799 (23:A3096)
 [7]
 M. J. E. GOLAY, "Note on complementary series," Proc. IRE, v. 50, 1962, p. 84. MR 0125799 (23:A3096)
 [8]
 R. J. TURYN, "Hadamard matrices, BaumerHall units, four symbol sequences, pulse compression and surface wave encodings," J. Combinatorial Theory Ser. A, v. 16, 1974, pp. 313333. MR 0345847 (49:10577)
 [9]
 S. JAUREGUI, JR., "Complementary sequences of length 26," IRE Trans. Information Theory, v. IT8, 1962, p. 323.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819760409235X
PII:
S 00255718(1976)0409235X
Article copyright:
© Copyright 1976 American Mathematical Society
