Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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 $ ( + 1, - 1)$-matrices of order $ n \equiv 2 \pmod 4$. 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.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 05B20

Retrieve articles in all journals with MSC: 05B20


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1976-0409235-X
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society