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Arasu, K. T., Bayes, Kyle, Nabavi, Ali. (1394). Nonexistence of two circulant weighing matrices of weight 81$^{1}$. , 4(3), 43-52. doi: 10.22108/toc.2015.6225
K. T. Arasu; Kyle Bayes; Ali Nabavi. "Nonexistence of two circulant weighing matrices of weight 81$^{1}$". , 4, 3, 1394, 43-52. doi: 10.22108/toc.2015.6225
Arasu, K. T., Bayes, Kyle, Nabavi, Ali. (1394). 'Nonexistence of two circulant weighing matrices of weight 81$^{1}$', , 4(3), pp. 43-52. doi: 10.22108/toc.2015.6225
Arasu, K. T., Bayes, Kyle, Nabavi, Ali. Nonexistence of two circulant weighing matrices of weight 81$^{1}$. , 1394; 4(3): 43-52. doi: 10.22108/toc.2015.6225

Nonexistence of two circulant weighing matrices of weight 81$^{1}$

Transactions on Combinatorics
مقاله 29، دوره 4، شماره 3، آذر 2015، صفحه 43-52    اصل مقاله (233.38 K)
نوع مقاله: 75th Birthday of G. B. Khosrovshahi
شناسه دیجیتال (DOI): 10.22108/toc.2015.6225
نویسندگان
K. T. Arasu* 1؛ Kyle Bayes1؛ Ali Nabavi2
1Wright State University
2Institute for Research in Fundamental Sciences (IPM)
چکیده
‎‎In this paper‎, ‎we prove the nonexistence of two weighing matrices of‎ ‎weight 81‎, ‎namely $CW(88,81)$ and $CW(99,81)$‎. ‎We will apply two‎ ‎very different methods to do so; for the case of $CW(88,81)$‎, ‎we‎ ‎will use almost purely counting methods‎, ‎while for $CW(99,81)$‎, ‎we‎ ‎will use algebraic methods‎.
کلیدواژه‌ها
weighing matrices؛ circulant؛ multipliers
مراجع

[1] K. T. Arasu and A. J. Gutman, Circulant weighing matrices, Cryptogr. Commun., 2 (2010) 155-171.

[2] K. T. Arasu, J. F. Dillon, D. Jungnickel and A. Pott, The solution of the waterloo problem, J. Combin. Theory Ser. A , 71 (1995) 316-331.

[3] K. T. Arasu and S. L. Ma, Abelian difference sets without self-conjugacy, Des. Codes Cryptogr., 15  (1998) 223-230.

[4] K. T. Arasu and D. K. Ray-Chaudhuri, Multiplier theorem for a difference list, Ars Combin., 22  (1986) 119-138.

[5] R. L. McFarland, On Multipliers of Abelian Difference Sets , PhD thesis, The Ohio State University, 1970.

[6] R. C. Mullin, A Note On Balanced Weighing Matrices, 452  of Lecture Notes in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York, 1975.

[7] Y. Strassler, The classi cation of circulant weighing matrices with weight 9 , PhD thesis, Bar-Ilan University, 1997.

[8] M. M. Tan, Circulant weighing matrices and multipliers , Preprint, 2014.

[9] M. M. Tan, Nonexistence of circulant weighing matrices of weight 36 and orders 60 , Preprint, (2014).

[10] V. Yorgov, On the existence of certain circulant weighing matrices, J. Combin. Math. Combin. Comput., 86  (2013) 73-85.

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