"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 7, 2016

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The error detection code based on the transformation of Christenson over the field GF(4)


V. A. Vershinin

Rybinsk state aviation technical University them. P. A. Solovyov


The paper is received on June 16, 2016

Abstract. The article discusses the spectral encoding based conversion of Christenson over the field GF(4). The purpose of the encoding is error detection. The effectiveness of encoding is evaluated in the case when the number of errors in code word larger than the number of guaranteed detectable errors. Simulation of the decoding process showed that the highest value of the probability of undetected error is obtained when the number of errors in the code word equal to the code distance. This probability is used in the article to estimate from above the probability of undetected error. If the number of errors in the code word is greater than or equal to the code distance, the  increase of the length of the code words under the condition of constant value of the code distance gives the opportunity to obtain an acceptable value of probability of undetected error.

Key words: spectral encoding, error detection, transformation of Christenson.


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