Maximal binary matrices and sum of two squares
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- by C. H. Yang PDF
- Math. Comp. 30 (1976), 148-153 Request permission
Abstract:
A maximal $( + 1, - 1)$-matrix of order 66 is constructed by a method of matching two finite sequences. This method also produced many new designs for maximal $( + 1, - 1)$-matrices of order 42 and new designs for a family of H-matrices of order ${26.2^n}$. A nonexistence proof for a $(\ast )$-type H-matrix of order 36, consequently for Golay complementary sequences of length 18, is also given.References
- Hartmut Ehlich, Determinantenabschätzungen für binäre Matrizen, Math. Z. 83 (1964), 123–132 (German). MR 160792, DOI 10.1007/BF01111249
- Joel Brenner and Larry Cummings, The Hadamard maximum determinant problem, Amer. Math. Monthly 79 (1972), 626–630. MR 301030, DOI 10.2307/2317092
- 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
- C. H. Yang, On designs of maximal $(+1,\,-1)$-matrices of order $n\equiv 2(\textrm {mod}\ 4)$. II, Math. Comp. 23 (1969), 201–205. MR 239748, DOI 10.1090/S0025-5718-1969-0239748-1
- C. H. Yang, On Hadamard matrices constructible by circulant submatrices, Math. Comp. 25 (1971), 181–186. MR 288037, DOI 10.1090/S0025-5718-1971-0288037-7
- Marcel J. E. Golay, Complementary series, IRE Trans. IT-7 (1961), 82–87. MR 0125799, DOI 10.1109/tit.1961.1057620
- Marcel J. E. Golay, Complementary series, IRE Trans. IT-7 (1961), 82–87. MR 0125799, DOI 10.1109/tit.1961.1057620
- 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 345847, DOI 10.1016/0097-3165(74)90056-9 S. JAUREGUI, JR., "Complementary sequences of length 26," IRE Trans. Information Theory, v. IT-8, 1962, p. 323.
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp. 30 (1976), 148-153
- MSC: Primary 05B20
- DOI: https://doi.org/10.1090/S0025-5718-1976-0409235-X
- MathSciNet review: 0409235