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@article{SEMR_2015_12_a56, author = {D. V. Chernikov}, title = {Error-correcting codes using biorthogonal filter banks}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {704--713}, publisher = {mathdoc}, volume = {12}, year = {2015}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a56/} }
D. V. Chernikov. Error-correcting codes using biorthogonal filter banks. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 704-713. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a56/
[1] G. Caire, R. L. Grossman, H. V. Poor, “Wavelet Transforms Associated with Finite Cyclic Groups”, IEEE Trans. Inf. Theory, 39:4 (1993), 1157–1166
[2] F. Fekri, R. M. Mersereau, R. W. Schafer, “Theory of wavelet transform over finite fields”, IEEE International Conference on Acoustics, Speech, and Signal Processing, Proceedings (1999), v. 3, 1999, 1213–1216
[3] F. Fekri, S. W. McLaughlin, R. M. Mersereau, R. W. Schafer, “Double Circulant Self-Dual Codes Using Finite-Field Wavelet Transforms”, Applied Algebra, Algebraic Algorithms and Error Correcting Codes Conference (Honolulu, HI, 1999), Lecture Notes in Comput. Sci., 1719, 1999, 355–364
[4] F. Fekri, S. W. McLaughlin, R. M. Mersereau, R. W. Schafer, Error Control Coding Using Finite-Field Wavelet Transforms, 30332, Center for Signal Image Processing, Georgia Institute of Technology, Atlanta, GA, 1999, 13 pp.
[5] S. Mallat, A Wavelet Tour of Signal Processing, Second Edition, Academic Press, 1999
[6] I. Doubechies, W. Sweldens, “Factoring Wavelet Transforms into Lifting Steps”, Journal of Fourier Analysis and Applications, 4:3 (1998), 247–269
[7] P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice-Hall, NJ, 1993
[8] A. K. Soman, P. P. Vaidyanathan, T. Q. Nquyen, “Linear-phase paraunitary filter banks: Theory, factorizations and designs”, IEEE Trans. Signal Processing, 41:12 (1993), 3480–3496
[9] S. M. Phoong, P. P. Vaidyanathan, “Paraunitary Filter Banks Over Finite Fields”, IEEE Trans. Signal Proc., 45:6 (1997), 1443–1457
[10] F. Fekri, R. M. Mersereau, R. W. Schafer, “Theory of paraunitary filter banks over fields of characteristic two”, IEEE Trans. Inform. Theory, 48:11 (2002), 2964–2979
[11] D. Chernikov, “Error-correcting codes using biorthogonal transforms over finite field”, Contemporary Problems of Mathematics and Its Applications, Conf. Proceedings (2011), IMM Ural Branch of RAS, Yekaterinburg, 2011, 247–249
[12] D. Chernikov, “Error-correcting codes using biorthogonal transforms over $GF(2^m)$”, Scientific session TUSUR, Conf. Proceedings (2012), v. 1, Tomsk State University of Control Systems and Radioelectronics, Tomsk, 2012, 17–20
[13] D. Chernikov, Biorthogonal coding algorithm implementations, SageMath Cloud Services, https://cloud.sagemath.com/projects/1ccf53b4-fab7-4a6d-9e8a-11495608d884/files/biorth-codes-construct.sagews