The polyphasic scheme of coding theory over fields of odd characteristic
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 3, pp. 77-85.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper presents the polyphasic scheme of the error-correcting coding based on two-channel filter set the exact recovery and the method of construction of codes with maximum code distance over fields of odd characteristic.
Keywords: error-correction coding, biorthogonal transform, biorthogonal set of filters, set of filters accurate recovery, wavelet-transform over a finite field.
@article{CHFMJ_2016_1_3_a5,
     author = {D. V. Chernikov},
     title = {The polyphasic scheme of coding theory over fields of odd characteristic},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {77--85},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_3_a5/}
}
TY  - JOUR
AU  - D. V. Chernikov
TI  - The polyphasic scheme of coding theory over fields of odd characteristic
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2016
SP  - 77
EP  - 85
VL  - 1
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_3_a5/
LA  - ru
ID  - CHFMJ_2016_1_3_a5
ER  - 
%0 Journal Article
%A D. V. Chernikov
%T The polyphasic scheme of coding theory over fields of odd characteristic
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2016
%P 77-85
%V 1
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_3_a5/
%G ru
%F CHFMJ_2016_1_3_a5
D. V. Chernikov. The polyphasic scheme of coding theory over fields of odd characteristic. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 3, pp. 77-85. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_3_a5/

[1] F. Fekri, S. W. McLaughlin, R. M. Mersereau, R. W. Schafer, Error control coding using finite-field wavelet transforms, Center for Signal Image Processing, Georgia Institute of Technology, Atlanta, GA, 30332, 1999, 13 pp.

[2] G. Caire, R. L. Grossman, H. V. Poor, “Wavelet transforms associated with finite cyclic groups”, IEEE Transactions on Information Theory, 39 (193), 1157–1166 | DOI | MR | Zbl

[3] F. Fekri, R. M. Mersereau, R. W. Schafer, “Theory of paraunitary filter banks over fields of characteristic two”, IEEE Transactions on Information Theory, 48 (2002), 2964–2979 | DOI | MR | Zbl

[4] S. M. Phoong, P. P. Vaidyanathan, “Paraunitary filter banks over finite fields”, IEEE Transactions on Signal Processing, 45 (1997), 1443–1457 | DOI | Zbl

[5] F. Fekri, S.\;W. McLaughlin, R. M. Mersereau, R. W. Schafer, “Decoding of half-rate wavelet codes, Golay code and more”, IEEE Intern. Conf. on Acoustics, Speech and Signal Processing (ICASSP), v. IV, 2001, 2609–2612

[6] F. Fekri, “Arbitrary rate maximum-distance separable wavelet codes”, IEEE Intern. Conf. on Acoustics, Speech and Signal Processing, v. 3, 2002, 2253–6

[7] D. V. Chernikov, “Error-correcting codes using biorthogonal filter banks”, Siberian Electronic Mathematical Reviews, 12 (2015), 704–713 (In Russ.) | Zbl

[8] S. Mallat, A wavelet tour of signal processing, 2nd edition, Academic Press, London, 1999, 637 pp. | MR | Zbl

[9] I. Doubechies, W. Sweldens, “Factoring wavelet transforms into lifting steps”, The J. of Fourier Analysis and Applications, 4:3 (1998), 247–269 | DOI | MR

[10] L. Welch, E. R. Berlekamp, Error correction for algebraic block codes, U.S. Patent 4,633.470. Sept. 27, 1983

[11] R. E. Blahut, Algebraic methods for signal processing and communications coding, Springer-Verlag, New York, 1992

[12] S. V. Fedorenko, “A simple algorithm for decoding algebraic codes”, Information and control systems, 2008, no. 3, 23–27

[13] D. Chernikov, Biorthogonal coding algorithm implementations, SageMath Cloud Services, (accessed 01.09.2016) https://cloud.sagemath.com/projects/1ccf53b4-fab7-4a6d-9e8a-11495608d884/files/biorth-codes-construct.sagews