MDS and NMDS Codes from the Extended Twisted Generalized Reed-Solomon Codes
For coding theorists, this provides new families of MDS and NMDS codes, but the contribution is incremental as it extends existing constructions.
This paper constructs extended twisted generalized Reed-Solomon codes and derives necessary and sufficient conditions for them to be MDS or NMDS codes, verifying results with examples.
This paper contributes to maximum distance separable (MDS) and near MDS (NMDS) properties of the extended generalized twisted Reed-Solomon (TGRS) codes. Firstly, a family of extended TGRS (ETGRS) are constructed by appending three columns to the generator matrix of original TGRS codes. Secondly, the necessary and sufficient conditions for these codes to be MDS or almost MDS (AMDS) codes are derived. Then, by analyzing the AMDS properties of their dual codes, the necessary and sufffcient conditions for them to be NMDS codes are established. Furthermore, some examples are given to verify the main results. Finally, we determine the non-generalized Reed-Solomon (non-GRS) characteristics of them via the Schur product method.