MODIFICATION OF PETERSON-GORENSTEIN-ZIERLER METHOD, BRINGING THE MATRIX TO TRIANGULAR FORM

F.G.Feyziyev, Dr Sc. (Phys.-Math.),
State University of Sumgait,
1 Baku St, 43th Quarter,  Sumgait, AZ5008, Azerbaidzhan, e-mail: FeyziyevFikratGul@gmail.com,
M.R. Mekhtiyeva, Cand. Sc. (Phys.-Math.),
State University of Baku,
23 Acad. Zakhid Khalilov St, Baku, AZ1148, Azerbaidzhan

Èlektron. model. 2018, 40(1):31-46
https://doi.org/10.15407/emodel.40.01.031

ABSTRACT

A modification of the Peterson-Gorenstein-Zierler method, based on the reduction of the matrix to triangular form, for detecting and correcting occurred errors in q-nary Bose-Chaudhuri-Hocquenghem codes has been proposed. The technique has been developed for accelerating calculation in accordance with this modification. An algorithm for decoding received messages based on the proposed modification is given.

KEYWORDS

q-nary Bose-Chaudhuri-Hocquenghem code, Peterson-Gorenstein-Zierler method, triangular matrix, primitive element of finite field, error locator.

REFERENCES

1. Blahut, R. (1986), Teoriya i praktika kodov, kontroliriyushikh oshibki [Theory and Practice of Error Control Codes], Translated by I.I. Grushina and V.M. Blinov, Mir, Moscow, Russia.
2. William, C.H. and Vera, P. (2003), Fundamentals of error-correcting codes, Cambridge University Press, Cambridge, UK.
3. Birkoff, G. and Barti, T. (1976), Sovremennaya prikladnaya algebra [Modern applied algebra], Translated by Yu.I. Manina, Mir, Moscow, Russia.
4. Feyziyev, F.G. (2015), “On one modification of algorithm Peterson–Gorenstein–Zierler and its effective realization”, Elektronnoe modelirovanie, Vol. 37, no. 3, pp. 3-16.
5. Feyziyev, F.G., Mekhtiyeva, M.R. and Samedova, Z.A. (2016), ”Modification of Peterson–Gorenstein–Zierler method, bringing the matrix to triangular form (binary case)”, Elektronnoe modelirovanie, Vol. 38, no. 5, pp. 11-21.
6. Feyziyev, F.G. and Babavand Arablou, M.A. (2012), “Description of decoding of p-nary cyclic codes in the class of sequential machines”, Izvestiya Natsionalnoy Akademii Nauk Azerbaydjana, Seriya Fiz.-Tekh. i Math. Nauk: Informatika i Problemy Upravleniya, Vol. XXXII, no. 6, pp. 3-9.

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