# MODIFICATION OF PETERSON-GORENSTEIN-ZIERLER METHOD, BRINGING THE MATRIX TO TRIANGULAR FORM (BINARY CASE)

F.G. Feyziyev, M.R. Mekhtiyeva, Z.A. Samedova

Èlektron. model. 2018, 38(5):11-22
https://doi.org/10.15407/emodel.38.05.011

### ABSTRACT

The theorem on the number of errors, which occurred in the received messages in the case of transmission of the binary Bose-Chaudhuri-Hocquenghem codes over communication channels, has been formulated. A modification of the Peterson-Gorenstein-Zierler method, based on the reduction of the matrix to triangular form, for detecting and correcting errors in the binary Bose-Chaudhuri-Hocquenghem codes has been proposed. The technique has been developed for accelerating calculation in accordance with this modification. A detailed description of the algorithm of decoding the received messages based on the above modifications and techniques is given.

### KEYWORDS

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

### REFERENCES

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https://doi.org/10.3103/S0146411612040037

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