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]**Hartmut Ehlich,*Determinantenabschätzungen für binäre Matrizen*, Math. Z.**83**(1964), 123–132 (German). MR**0160792**, https://doi.org/10.1007/BF01111249**[2]**Joel Brenner and Larry Cummings,*The Hadamard maximum determinant problem*, Amer. Math. Monthly**79**(1972), 626–630. MR**0301030**, https://doi.org/10.2307/2317092**[3]**Richard J. Turyn,*Complex Hadamard matrices*, Combinatorial Structures and their Applications (Proc. Calgary Internat. Conf., Calgary, Alta., 1969) Gordon and Breach, New York, 1970, pp. 435–437. MR**0270938****[4]**C. H. Yang,*On designs of maximal (+1,-1)-matrices of order 𝑛≡2(𝑚𝑜𝑑4). II*, Math. Comp.**23**(1969), 201–205. MR**0239748**, https://doi.org/10.1090/S0025-5718-1969-0239748-1**[5]**C. H. Yang,*On Hadamard matrices constructible by circulant submatrices*, Math. Comp.**25**(1971), 181–186. MR**0288037**, https://doi.org/10.1090/S0025-5718-1971-0288037-7**[6]**Marcel J. E. Golay,*Complementary series*, IRE Trans.**IT-7**(1961), 82–87. MR**0125799****[7]**Marcel J. E. Golay,*Complementary series*, IRE Trans.**IT-7**(1961), 82–87. MR**0125799****[8]**R. J. Turyn,*Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compression, and surface wave encodings*, J. Combinatorial Theory Ser. A**16**(1974), 313–333. MR**0345847****[9]**S. JAUREGUI, JR., "Complementary sequences of length 26,"*IRE Trans. Information Theory*, v. IT-8, 1962, p. 323.

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

Article copyright:
© Copyright 1976
American Mathematical Society