Sum-Rank BCH Codes and Cyclic-Skew-Cyclic Codes

In this work, cyclic-skew-cyclic codes and sum-rank BCH are introduced. Cyclic-skew-cyclic characterized as left ideals of a suitable non-commutative finite ring, constructed using skew polynomials on top (or vice versa). Single generators such found, they used to construct generator matrices the corresponding codes. The notion defining set is introduced, pairs roots poynomials. A lower bound (called bound) minimum distance given for whose contains certain consecutive pairs. Sum-rank codes, with prescribed distance, then defined largest code described, its dimension obtained. Thanks it, tables provided showing that beat previously known metric binary 2 ×2 (i.e., codewords lists matrices, wide range list lengths correspond length). Finally, decoder up half their