Maximal binary matrices and sum of two squares

Author:
C. H. Yang

Journal:
Math. Comp. **30** (1976), 148-153

MSC:
Primary 05B20

DOI:
https://doi.org/10.1090/S0025-5718-1976-0409235-X

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 *H*-matrices of order . A nonexistence proof for a -type *H*-matrix of order 36, consequently for Golay complementary sequences of length 18, is also given.

**[1]**H. EHLICH, "Determinantenabschä'tzungen für binäre Matrizen,"*Math. Z.*, v. 83, 1964, pp. 123-132. MR**28**#4003. MR**0160792 (28:4003)****[2]**J. BRENNER & L. CUMMINGS, "The Hadamard maximum determinant problem,"*Amer. Math. Monthly*, v. 79, 1972, pp. 626-630. 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. 435-437. 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. 201-205. MR**0239748 (39:1105)****[5]**C. H. YANG, "On Hadamard matrices constructible by circulant submatrices,"*Math. Comp.*, v. 25, 1971, pp. 181-186. MR**44**#5235. MR**0288037 (44:5235)****[6]**M. J. E. GOLAY, "Complementary series,"*IRE Trans. Information Theory*, v. IT-7, 1961, pp. 82-87. 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, Baumer-Hall units, four symbol sequences, pulse compression and surface wave encodings,"*J. Combinatorial Theory Ser. A*, v. 16, 1974, pp. 313-333. MR**0345847 (49:10577)****[9]**S. JAUREGUI, JR., "Complementary sequences of length 26,"*IRE Trans. Information Theory*, v. IT-8, 1962, p. 323.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0409235-X

Article copyright:
© Copyright 1976
American Mathematical Society