Error correction by Reed–Solomon codes using its automorphisms

The article explores the syndrome invariants of АГ-group automorphisms Reed–Solomon codes (RS-codes) that are a joint group affine and cyclic permutations. found real set norms N Г-orbits make up one or another АГ-orbit. vectors with 2 1 Cδ− coordinates from Galois field, determined by all kinds pairs components error syndromes. In this form, АГ-orbits were cumbersome difficult to use. Therefore, their replacement conditional partial is proposed. These quasi-invariants called norm-projections. Norm-projection uniquely identifies its АГ-orbit therefore serves as an adequate way for formulating correction method RS-codes based on АГ-orbits. power estimated value N2, equal square length RS-code. search in transmitted messages new reduced parsing АГ‑orbits, but actually norm-projections, subsequent these errors within particular proposed works almost N2 times faster than traditional methods, operating basic “syndrome – error” principle, boils down entire until specific vector found.