DISTRIBUTED COMPUTER NETWORK FOR COMPUTATION OF WEIGHT SPECTRA FOR SOME ERROR CONTROL CODES

Martin Rakús - Jozef Oboňa - Peter Farkaš - Ladislav Divinec - Pavol Čižmárik

   Error control codes (ECC) are used today in variety of different applications in the area of communications. Recently some new linear block codes defined over finite fields were constructed. Newly found codes have higher code rate (smaller redundancy) than widely used Reed Solomon codes constructed over the same finite field. Error correcting capabilities of ECC is determined by the code distance d_m. In order to determine the code distance for proposed codes a complete weight spectrum has to be calculated, because analytical solution of weight spectra determination for mention codes does not exist. Since the number of codewords in each of the found codes is very high (up to 16²³⁵, if constructed over GF(16)) direct calculation of weight spectra of such codes is therefore infeasible. Using the relationships between original code and its dual significantly simplifies the problem, but computational complexity is still too high to be computed on a single PC. Therefore to overcome the computational complexity it was necessary to use some structural knowledge and also to built an appropriate computer network architecture for distributed computing. In this paper the practical approach to calculation of the weight spectra is described.

Keywords: distributed computing, linear block code, finite field, Reed Solomon codes, code rate, code distance, error control code

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