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On base and Turyn sequences


Authors: C. Koukouvinos, S. Kounias and K. Sotirakoglou
Journal: Math. Comp. 55 (1990), 825-837
MSC: Primary 62K10
DOI: https://doi.org/10.1090/S0025-5718-1990-1023764-7
MathSciNet review: 1023764
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Abstract: Base sequences of lengths $ n + 1$, $ n + 1$, n, n are constructed for all decompositions of $ 4n + 2$ into four squares for $ n = 19, \ldots ,24$. The construction is achieved through an algorithm which is also presented. It is proved through an exhaustive search that Turyn sequences do not exist for $ n = 18, \ldots ,27$; since Turyn sequences cannot exist for $ n = 28$ or 29, the first unsettled case is $ n = 30$.


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

  • [1] G. Cohen, D. Rubie, J. Seberry, C. Koukouvinos, S. Kounias, and M. Yamada, A survey of base sequences, disjoint complementary sequences and $ OD(4t;t,t,t,t)$, J. Combin. Math. and Combin. Computing 5 (1989), 60-104. MR 993883 (90e:05021)
  • [2] J. Cooper and J. Wallis, A construction for Hadamard arrays, Bull. Australian Math. Soc. 7 (1972), 269-277. MR 0316271 (47:4819)
  • [3] A. V. Geramita and J. Seberry, Orthogonal designs: Quadratic forms and Hadamard matrices, Marcel Dekker, New York-Basel, 1979. MR 534614 (82a:05001)
  • [4] C. Koukouvinos, S. Kounias, and J. Seberry, Further results on base sequences, disjoint complementary sequences, $ OD(4t;t,t,t,t)$ and the excess of Hadamard matrices, Ars Combin. (to appear). MR 1088294 (91m:05037)
  • [5] R. J. Turyn, Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compressions and surface wave encodings, J. Combin. Theory Ser. A 16 (1974), 313-333. MR 0345847 (49:10577)
  • [6] C. H. Yang, A composition theorem for $ \delta $-codes, Proc. Amer. Math. Soc. 89 (1983), 375-378. MR 712655 (85i:94025)
  • [7] -, On composition of four-symbol $ \delta $-codes and Hadamard matrices, Proc. Amer. Math. Soc. 107 (1989), 763-776. MR 979054 (90e:94043)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1990-1023764-7
Keywords: Associate polynomial, algorithm, autocorrelation, cross-correlation, construction
Article copyright: © Copyright 1990 American Mathematical Society

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