Abstract
Our main objective is to show that the computational methods, developed previously to search for difference families in cyclic groups, can be fully extended to the more general case of arbitrary finite abelian groups. In particular the power spectral density test and the method of compression can be used to help the search.
References
[1] K. T. Arasu, Q. Xiang, On the existence of periodic complementary binary sequences, Des. Codes Cryptogr. 2 (1992), 257–262.10.1007/BF00141970Search in Google Scholar
[2] R. Craigen, H. Kharaghani, Hadamard matrices and Hadamard designs, in Handbook of Combinatorial Designs, 2nd ed. C. J. Colbourn, J. H. Dinitz (eds) pp. 273–280. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2007.Search in Google Scholar
[3] D. Ž. —Doković,. I. S. Kotsireas, D-optimal matrices of orders 118, 138, 150, 154 and 174. In: C. J. Colbourn (ed.) Algebraic Design Theory and Hadamard Matrices, pp. 71–82, ADTHM, Lethbridge, Alberta, Canada, July 2014. Springer Proceedings in Mathematics & Statistics, vol. 133. Springer 2015.10.1007/978-3-319-17729-8_6Search in Google Scholar
[4] D. Ž. —Doković, I. S. Kotsireas, Compression of periodic complementary sequences and applications, Des. Codes Cryptogr. 74 (2015), 365–377.10.1007/s10623-013-9862-zSearch in Google Scholar
[5] D. Ž.—Doković, I. S. Kotsireas, Periodic Golay pairs of length 72. In: C. J. Colbourn (ed.) Algebraic Design Theory and Hadamard Matrices, pp. 83–92, ADTHM, Lethbridge, Alberta, Canada, July 2014. Springer Proceedings in Mathematics & Statistics, vol. 133. Springer 2015.10.1007/978-3-319-17729-8_7Search in Google Scholar
[6] D. Ž. —Doković, I. S. Kotsireas, Goethals-Seidel difference families with symmetric or skew base blocks, Math. Comput. Sci. (2018) 12:373–388. Springer.10.1007/s11786-018-0381-1Search in Google Scholar
[7] R. J. Fletcher, M. Gysin, J. Seberry, Application of the discrete Fourier transform to the search for generalised Legendre pairs and Hadamard matrices. Australas. J. Combin. 23 (2001), 75–86.Search in Google Scholar
[8] H. Kharaghani, C. Koukouvinos, Complementary, Base and Turyn Sequences, in Handbook of Combinatorial Designs, 2nd ed. C. J. Colbourn, J. H. Dinitz (eds) pp. 317–321. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2007.Search in Google Scholar
[9] H. Kharaghani, W. Orrick, D-optimal matrices, in Handbook of Combinatorial Designs, 2nd ed. C. J. Colbourn, J. H. Dinitz (eds) pp. 296–298. Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, 2007.Search in Google Scholar
[10] B. Luong, Fourier Analysis on Finite Abelian Groups, Birkhäuser Boston, 2009.10.1007/978-0-8176-4916-6Search in Google Scholar
[11] J. Seberry, M. Yamada, Hadamard matrices, sequences, and block designs. In Contemporary design theory, 431–560, Wiley-Intersci. Ser. Discrete Math. Optim., Wiley, New York, 1992.Search in Google Scholar
[12] A. Terras, Fourier Analysis on Finite Groups and Applications, London Mathematical Society Student Texts 43, Cambridge University Press, 1999.Search in Google Scholar
[13] J. Wallis, A. L. Whiteman, Some classes of Hadamard matrices with constant diagonal, Bull. Austral. Math. Soc. 7 (1972), 233–249.10.1017/S0004972700044993Search in Google Scholar
© 2019 Dragomir Ž. Ðoković et al., published by De Gruyter Open
This work is licensed under the Creative Commons Attribution 4.0 International License.