Williamson Hadamard matrices and Gauss sums

Koichi YAMAMOTO; Mieko YAMADA

doi:10.2969/jmsj/03740703

Koichi YAMAMOTO, Mieko YAMADA

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JOURNAL FREE ACCESS

1985 Volume 37 Issue 4 Pages 703-717

DOI https://doi.org/10.2969/jmsj/03740703

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Published: 1985 Received: January 17, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. S. Agayan and A. G. Sarukhanyan, Recurrence formulas for the construction of Williamson-type matrices, Math. Notes, 30 (1982), 796-804.
2) H. Davenport and H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. Reine Angew. Math., 172 (1935), 151-182.
3) A. V. Geramita and J. Seberry, Orthogonal Designs : Quadratic Forms and Hadamard Matrices, Lecture Notes in Pure and Applied Math., 45, Marcel Dekker, New York and Basel, 1979.
4) Z. Kiyasu, Hadamard matrix and its applications, Denshi-Tsushin Gakkai, Tokyo, 1980, (in Japanese).
5) S. Lang, Cyclotomic Fields, Springer-Verlag, New York. Heidelberg-Berlin, 1978.
6) K. Sawade, Hadamard matrices of order 100 and 108, Bull. Nagoya Inst. Technology, 29 (1977), 147-153.
7) T. Storer, Cyclotomy and Difference Sets, Markham Publishing Company, Chicago, 1967.
8) R. J. Turyn, An infinite class of Williamson matrices, J. Combinatorial Theory Ser. A, 12 (1972), 319-321.
9) W. D. Wallis, A. P. Street and J. S. Wallis, Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices, Lecture Notes in Math., 292, Springer-Verlag, 1972.
10) A. L. Whiteman, An infinite family of Hadamard matrices of Williamson type, J. Combinatorial Theory Ser. A, 14 (1973), 334-340.
11) M. Yamada, On Gauss sums in a finite field and their applications to Hadamard matrices, Reports of symposium on algebraic number theory held at University of Tokyo, Oct. 17-19, 1983, 9-30, (in Japanese).
12) K. Yamamoto, A generalized Williamson equation, Colloq. Math. Soc. János Bolyai, 37 (1983), 839-850.

Right : [1] S. S. Agayan and A. G. Sarukhanyan, Recurrence formulas for the construction of Williamson-type matrices, Math. Notes, 30 (1982), 796-804.
[2] H. Davenport and H. Hasse, Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. Reine Angew. Math., 172 (1935), 151-182.
[3] A. V. Geramita and J. Seberry, Orthogonal Designs: Quadratic Forms and Hadamard Matrices, Lecture Notes in Pure and Applied Math., 45, Marcel Dekker, New York and Basel, 1979.
[4] Z. Kiyasu, Hadamard matrix and its applications, Denshi-Tsushin Gakkai, Tokyo, 1980, (in Japanese).
[5] S. Lang, Cyclotomic Fields, Springer-Verlag, New York-Heidelberg-Berlin, 1978.
[6] K. Sawade, Hadamard matrices of order 100 and 108, Bull. Nagoya Inst. Technology, 29 (1977), 147-153.
[7] T. Storer, Cyclotomy and Difference Sets, Markham Publishing Company, Chicago, 1967.
[8] R. J. Turyn, An infinite class of Williamson matrices, J. Combinatorial Theory Ser. A, 12 (1972), 319-321.
[9] W. D. Wallis, A. P. Street and J. S. Wallis, Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices, Lecture Notes in Math., 292, Springer-Verlag, 1972.
[10] A. L. Whiteman, An infinite family of Hadamard matrices of Williamson type, J. Combinatorial Theory Ser. A, 14 (1973), 334-340.
[11] M. Yamada, On Gauss sums in a finite field and their applications to Hadamard matrices, Reports of symposium on algebraic number theory held at University of Tokyo, Oct. 17-19, 1983, 9-30, (in Japanese).
[12] K. Yamamoto, A generalized Williamson equation, Colloq. Math. Soc. János Bolyai, 37 (1983), 839-850.

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