Coding and decoding of systematic Reed-Solomon codes by method, which alternative of algorithm of Peterson-Gorenstein-Zirler

Abstract

Reed-Solomon codes are effective and widely used in many fields of science and technology related to noise-immune conversion (reception-transmission) of digital information. Since the advent of (1960) and up to now, the description of the PC-code, including the synthesis of code words, as well as the localization and elimination of errors, is based on the use of formal elements, which are the roots of gen-erator, information and test polynomials. The congestion of technological operations by algebraic elements is to a certain extent "ballast", which not only complicates the computation process in the hardware-software implemen-tation, but also creates certain difficulties in the study of PC-encoding and decoding algorithms. In this regard, the paper proposes a variant of constructing PC-codes, greatly simplifying both the mastering of the algorithm itself and the process of detecting and eliminating errors in distorted data. Proposals are based on the transfer of transfor-mations from the space of originals to the space of an iso-morphic image. As a result of the proposed replacement, the computational process turns out to be reduced to sim-ple operations of modular arithmetic over integer operands easily realized by computer hardware.