Abstract
The paper studies a generalized Hadamard matrix H = (g i j) of order n with entries gi j from a group G of order n. We assume that H satisfies: (i) For m ≠ k, G = {g m i g k i -1∣ i = 1,...., n} (ii) g 1i = g i1 = 1 for each i; (iii) g ij -1 = g ji for all i, j. Conditions (i) and (ii) occur whenever G is a(P, L) -transitivity for a projective plane of order n. Condition (iii) holds in the case that H affords a symmetric incidence matrix for the plane. The paper proves that G must be a 2-group and extends previous work to the case that n is a square.
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References
C. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience, New York (1966).
P. Dembowski, Finite Geometries, Springer-Verlag, Berlin-Heidelberg, New York (1968).
P. Dey and J. Hayden, On symmetric incidence matrices of projective planes, Designs, Codes and Cryptography, Vol. 6 (1995) pp. 179–188.
D. Gorenstein, Finite Groups, Harper and Row, New York (1968).
J. Hayden, Elementary abelian cartesian groups, Can. J. Math., Vol XL,No. 6 (1988) pp. 83–92.
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Hayden, J.L. Generalized Hadamard Matrices. Designs, Codes and Cryptography 12, 69–73 (1997). https://doi.org/10.1023/A:1008245910019
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DOI: https://doi.org/10.1023/A:1008245910019