Most of the codes that have an algebraic decoding algorithm are derived from the Reed Solomon codes. They are obtained by taking equivalent codes, for example the generalized Reed Solomon codes, or by using the so-called subfield subcode method, which leads to Alternant codes and Goppa codes over the underlying prime field, or over some intermediate subfield. The main advantages of these constr...

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. Therefor...

We provide an algebraic description for sum-rank metric codes, as quotient space of a skew polynomial ring. This approach generalizes at the same time group algebra setting rank-metric codes and in Hamming metric. allows to construct twisted linearized Reed-Solomon new family maximum distance extending Sheekey's Gabidulin rank Furthermore, we analogue Trombetti-Zhou construction, which also pro...

List-decodability of Reed–Solomon codes has received a lot attention, but the best-possible dependence between parameters is still not well-understood. In this work, we focus on case where list-decoding radius form $r=1-\varepsilon $ ...