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In digital communication and storage systems, the exchange of data is achieved using a communication channel which is not completely reliable. Therefore, detection and correction of possible errors are required by adding redundant bits to information data. Several algebraic and heuristic decoders were designed to detect and correct errors. The Hartmann Rudolph (HR) algorithm enables to decode a sequence symbol by symbol. The HR algorithm has a high complexity, that's why we suggest using it partially with the algebraic hard decision decoder Berlekamp-Massey (BM). In this work, we propose a concatenation of Partial Hartmann Rudolph (PHR) algorithm and Berlekamp-Massey decoder to decode BCH (Bose-Chaudhuri-Hocquenghem) codes. Very satisfying results are obtained. For example, we have used only 0.54% of the dual space size for the BCH code (63,39,9) while maintaining very good decoding quality. To judge our results, we compare them with other decoders.

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In this paper, the authors present a concatenation of Hartmann and Rudolph (HR) partially exploited and a decoder based on hash techniques and syndrome calculation to decode linear block codes. This work consists firstly to use the HR with a reduced number of codewords of the dual code then the HWDec which exploits the output of the HR partially exploited. Researchers have applied the proposed decoder to decode some Bose, Chaudhuri, and Hocquenghem (BCH) and quadratic residue (QR) codes. The simulation and comparison results show that the proposed decoder guarantees very good performances, compared to several competitors, with a much-reduced number of codewords of the dual code. For example, for the BCH(31, 16, 7) code, the good results found are based only on 3.66% of the all codewords of the dual code space, for the same code the reduction rate of the run time varies between 78% and 90% comparing to the use of Hartmann and Rudolph alone. This shows the efficiency, the rapidity, and the reduction of the memory space necessary for the proposed concatenation.