Multi twisted codes over finite fields and their generalizations

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Nowadays error-correcting codes are widely used in communication systems, re-turning pictures from deep space, designing registration numbers, and storage of data in memory systems. An important family of error-correcting codes is that of linear codes, which contain many well-known codes such as Hamming codes, Hadamard codes, cyclic codes and quasi-cyclic codes. Recently, Aydin and Halilovic¿ [5] introduced and studied multi-twisted (MT) codes over the ¿nite ¿eld Fq, whose block lengths are coprime to q. These codes are generalizations of well-known classes of linear codes, such as constacyclic codes and generalized quasi-cyclic codes, hav-ing rich algebraic structures and containing record-breaker codes. In the same work, they obtained subcodes of MT codes with best-known parameters [33, 12, 12] over F3, [53, 18, 21] over F5, [23, 7, 13] over F7 and optimal parameters [54, 4, 44] over F7. Apart from this, they proved that the code parameters [53, 18, 21] over F5 and [33, 12, 12] over F3 can not be attained by constacyclic and quasi-cyclic codes, which suggests that this larger class of MT codes is more promising to ¿nd codes with better parameters than the current best known linear codes.