Geodesic
Properties and applications of $G$-orbits polynomial invariants of errors in reverse codes
Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2018), pp. 21-28.

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

In this paper is described a two-step procedure for polynomial-norm error correction with reverse error correcting codes. Such codes of length n traditionally are defined by check matrix $H_{R}=(\beta^{i},\beta^{-i})^{T}, 0\leq i\leq n-1, \beta=\alpha^{\frac{2^{m}-1}{n}}$ and $\alpha$ is primitive element of $GF(2^{m})$. Also in paper you can find a description of error correction algorithm and an example based on reverse code of length $89$.
Keywords: error correcting codes; code minimal distance; reverse codes; BCH codes; norm method of error correction. 
@article{BGUMI_2018_3_a2,
     author = {A. V. Kushnerov and V. A. Lipnitski},
     title = {Properties and applications of $G$-orbits polynomial invariants of errors in reverse codes},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {21--28},
     publisher = {mathdoc},
     volume = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2018_3_a2/}
}
TY  - JOUR
AU  - A. V. Kushnerov
AU  - V. A. Lipnitski
TI  - Properties and applications of $G$-orbits polynomial invariants of errors in reverse codes
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2018
SP  - 21
EP  - 28
VL  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2018_3_a2/
LA  - ru
ID  - BGUMI_2018_3_a2
ER  - 
%0 Journal Article
%A A. V. Kushnerov
%A V. A. Lipnitski
%T Properties and applications of $G$-orbits polynomial invariants of errors in reverse codes
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2018
%P 21-28
%V 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2018_3_a2/
%G ru
%F BGUMI_2018_3_a2
A. V. Kushnerov; V. A. Lipnitski. Properties and applications of $G$-orbits polynomial invariants of errors in reverse codes. Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2018), pp. 21-28. http://geodesic.mathdoc.fr/item/BGUMI_2018_3_a2/

[1] FDzh. Mak-Vilyams, N. Sloen, “Teoriya kodov, ispravlyayuschikh oshibki”, Moskva: Svyaz, 1979

[2] V. K. Konopelko, V. A. Lipnitskii, “Teoriya norm sindromov i perestanovochnoe dekodirovanie pomekhoustoichivykh kodov”, Moskva: Editorial URSS, 2004

[3] V. K. Konopelko, V. A. Lipnitskii, “Normennoe dekodirovanie pomekhoustoichivykh kodov i algebraicheskie uravneniya”, Minsk: Izdatelskii tsentr BGU, 2007

[4] V. A. Lipnitskii, “Teoriya norm sindromov”, Minsk: BGUIR, 2010

[5] V. A. Lipnitskii, A. V. Kushnerov, “Nekotorye svoistva reversivnykh pomekhoustoichivykh kodov. Tekhnologii informatizatsii i upravleniya”, Minsk: RIVSh, 2017, 47–54

[6] V. A. Lipnitskii, A. V. Kushnerov, “Svoistva i dekodirovanie reversivnykh kodov s konstruktivnym rasstoyaniem 5”, Vesnik Magileuskaga dzyarzhaunaga universiteta imya AA Kulyashova, 2 (2016), 30–44

[7] V. A. Lipnitskii, E. V. Sereda, “Polinomialnye invarianty G-orbit oshibok BChKh-kodov i ikh primenenie”, Doklady BGUIR, 5(107) (2017), 62–69

[8] V. A. Lipnitskii, “Sovremennaya prikladnaya algebra. Matematicheskie osnovy zaschity informatsii ot pomekh i nesanktsionirovannogo dostupa”, Minsk: BGUIR, 2005, 88

[9] R. Liddl, G. Niderraiter, “Konechnye polya”, Moskva: Mir, 1988 | MR