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Hadamard matrices of composite orders | ||
| Transactions on Combinatorics | ||
| دوره 13، شماره 1، خرداد 2024، صفحه 31-40 اصل مقاله (437.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2022.133659.1989 | ||
| نویسندگان | ||
| Tianbing Xia* 1؛ Guoxin Zuo2؛ Liantang Lou3؛ Mingyuan Xia2 | ||
| 1School of Computing and Information Technology, University of Wollongong Australia, Wollongong, Australia | ||
| 2School of Mathematics and Statistics, Central China Normal University, Wuhan, China | ||
| 3College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, China | ||
| چکیده | ||
| In this paper, we give a method for the constructions of Hadamard matrices of composite orders by using suitable $T$-matrices and known Hadamard matrices. We establish a formula for $T$-matrices and Hadamard matrices and discuss under what condition we can get $T$-matrices from the known Hadamard matrices. | ||
| کلیدواژه‌ها | ||
| Composite Hadamard matrix؛ $T$-matrix؛ Hadamard matrix؛ Suitable matrices | ||
| مراجع | ||
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[1] Y. Q. Chen, On the existence of Abelian Hadamard difference sets and a new family of difference sets, Finite Fields Appl., 3 (1997) 234–256. [2] C. Koukouvinos, Base sequence of length m + p, m + p, m, m for p = 1 and 0 ≤ 0 ≤ 35, and p = 2t − 1, m = 2t, 13 ≤ t ≤ 17, Personal communication. [3] J. Seberry and M. Yamada, Hadamard matrices, sequences, and block designs in Contemporary Design Theory, Wiley, New York, 1992 431–560. [4] M. Xia, Some infinite classes of special Williamson matrices and difference sets, J. Comb. Theory, Ser. A, 61 (1992) 230–242. [5] M. Xia and T. Xia, Hadamard matrices constructed from supplementary difference sets in the class H1 , J. Comb. Des., 2 (1994) 325–339. [6] M. Xia and T. Xia, A family of C-partitions and T -matrices, J. Comb. Des., 7 (1999) 269–281.
[7] M. Xia, T. Xia and J. Seberry, A new method for Constructing Williamson matrices, Des. Codes Cryptog- raphy, 35 (2005) 191–209. [8] T. Xia, G. Zuo and M. Xia, 2 Families of negacyclic matrices, Far East Journal of Mathematical Science, 129 (2021) 131–146. [9] T. Xia, J. Seberry and M. Xia, Some new constructions of orthogonal designs, Australas. J. Comb., 55 (2013) 121–130. [10] G. Zuo and T. Xia, A special class of T -matrices, Des. Codes Cryptography, 54 (2010) 21–28.
[11] G. Zuo, M. Xia and T. Xia, Constructions of composite T -matrices, Linear Algebra Appl., 438 (2013) 1223–1228. [12] H. Gholamiangonabadi, Amicable T -matrices and Applications, M. Sc. Thesis, University of Lethbridge, Alberta, Canada, 2012 | ||
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