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Algorithms for finding inverse of two patterned matrices over \(\mathbb{Z}_p\). (English) Zbl 1474.94067

Summary: Circulant matrix families have become an important tool in network engineering. In this paper, two new patterned matrices over \(\mathbb{Z}_p\) which include row skew first-plus-last right circulant matrix and row first-plus-last left circulant matrix are presented. Their basic properties are discussed. Based on Newton-Hensel lifting and Chinese remaindering, two different algorithms are obtained. Moreover, the cost in terms of bit operations for each algorithm is given.

MSC:

94A60 Cryptography

References:

[1] Basic, M., Which weighted circulant networks have perfect state transfer?, Information Sciences, 257, 193-209 (2014) · Zbl 1322.81013 · doi:10.1016/j.ins.2013.09.002
[2] Noual, M.; Regnault, D.; Sené, S., About non-monotony in Boolean automata networks, Theoretical Computer Science, 504, 12-25 (2013) · Zbl 1297.68179 · doi:10.1016/j.tcs.2012.05.034
[3] Caudrelier, V.; Mintchev, M.; Ragoucy, E., Quantum wire network with magnetic flux, Physics Letters A, 377, 31-33, 1788-1793 (2013) · Zbl 1302.82139 · doi:10.1016/j.physleta.2013.05.018
[4] Aguiar, M. A. D.; Ruan, H., Interior symmetries and multiple eigenvalues for homogeneous networks, SIAM Journal on Applied Dynamical Systems, 11, 4, 1231-1269 (2012) · Zbl 1260.34066 · doi:10.1137/110851183
[5] Zhang, C.; Dangelmayr, G.; Oprea, I., Storing cycles in Hopfield-type networks with pseudoinverse learning rule: admissibility and network topology, Neural Networks, 46, 283-298 (2013) · Zbl 1296.68154 · doi:10.1016/j.neunet.2013.06.008
[6] Coetzee, J. C.; Cordwell, J. D.; Underwood, E.; Waite, S. L., Single-layer decoupling networks for circulant symmetric arrays, IETE Technical Review, 28, 3, 232-239 (2011) · doi:10.4103/0256-4602.81235
[7] Wang, G.; Cheng, S. S., 6-periodic travelling waves in an artificial neural network with bang-bang control, Journal of Difference Equations and Applications, 18, 2, 261-304 (2012) · Zbl 1242.49011 · doi:10.1080/10236190903460396
[8] Pais, D.; Caicedo-Núñez, C. H.; Leonard, N. E., Hopf bifurcations and limit cycles in evolutionary network dynamics, SIAM Journal on Applied Dynamical Systems, 11, 4, 1754-1784 (2012) · Zbl 1257.91008 · doi:10.1137/120878537
[9] Cho, Y.; Chung, I., A parallel routing algorithm on circulant networks employing the Hamiltonian circuit Latin square, Information Sciences, 176, 21, 3132-3142 (2006) · Zbl 1103.68016 · doi:10.1016/j.ins.2005.12.014
[10] Grassi, G., On the design of discrete-time cellular neural networks with circulant matrices, International Journal of Circuit Theory and Applications, 28, 193-202 (2000) · Zbl 1054.93507
[11] Wu, J., Symmetric functional-differential equations and neural networks with memory, Transactions of the American Mathematical Society, 350, 12, 4799-4838 (1998) · Zbl 0905.34034 · doi:10.1090/S0002-9947-98-02083-2
[12] Gao, F.; Jiang, B.; Gao, X.; Zhang, X., Superimposed training based channel estimation for OFDM modulated amplify-and-forward relay networks, IEEE Transactions on Communications, 59, 7, 2029-2039 (2011) · doi:10.1109/TCOMM.2011.051711.100431
[13] Wang, G.; Gao, F.; Wu, Y.; Tellambura, C., Joint CFO and channel estimation for OFDM-based two-way relay networks, IEEE Transactions on Wireless Communications, 10, 2, 456-465 (2011) · doi:10.1109/TWC.2010.120310.091615
[14] Chillag, D., Regular representations of semisimple algebras, separable field extensions, group characters, generalized circulants, and generalized cyclic codes, Linear Algebra and Its Applications, 218, 147-183 (1995) · Zbl 0839.20015 · doi:10.1016/0024-3795(93)00167-X
[15] Bini, D.; Corso, G. M. D.; Manzini, G.; Margara, L., Inversion of circulant matrices over Zm, Mathematics of Computation, 70, 1169-1182 (2000) · Zbl 0977.65022
[16] Dong, H.; Wang, Z.; Gao, H., Distributed \(H_∞\) filtering for a class of markovian jump nonlinear time-delay systems over lossy sensor networks, IEEE Transactions on Industrial Electronics, 60, 10, 4665-4672 (2013) · doi:10.1109/TIE.2012.2213553
[17] Wang, Z.; Dong, H.; Shen, B.; Gao, H., Finite-horizon \(H_\infty\) filtering with missing measurements and quantization effects, IEEE Transactions on Automatic Control, 58, 7, 1707-1718 (2013) · Zbl 1369.93660 · doi:10.1109/TAC.2013.2241492
[18] Ding, D.; Wang, Z.; Hu, J.; Shu, H., Dissipative control for state-saturated discrete time-varying systems with randomly occurring nonlinearities and missing measurements, International Journal of Control, 86, 4, 674-688 (2013) · Zbl 1278.93279 · doi:10.1080/00207179.2012.757652
[19] Hu, J.; Wang, Z.; Shen, B.; Gao, H., Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements, International Journal of Control, 86, 4, 650-663 (2013) · Zbl 1278.93269 · doi:10.1080/00207179.2012.756149
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