Two new families of linear codes are built from modified GRS generator matrices, producing non-GRS MDS codes with derived parity-check matrices and self-duality conditions.
Column Twisted Reed-Solomon Codes as MDS Codes
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abstract
In this paper, we study column twisted Reed-Solomon(TRS) codes. We establish some sufficient conditions for these codes to be MDS and show that the dimension of their Schur square codes is $2k$. Consequently, these TRS codes are shown to be not equivalent to Reed-Solomon(RS) codes. Moreover, our construction offers more flexible parameters than existing twisted generalized Reed-Solomon(TGRS) code designs. For a large odd prime power $q$, systematically constructed TGRS codes are known to be limited to length $\frac{q+1}{2}$. By contrast, our column TRS construction supports code lengths up to $\frac{q+3}{2}$. Finally, we present the dual codes of column TRS codes. Overall, this work introduces a new method for constructing MDS codes by appending column vectors to some generator matrix of an RS code.
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Two Families of Linear Codes Containing Non-GRS MDS Codes
Two new families of linear codes are built from modified GRS generator matrices, producing non-GRS MDS codes with derived parity-check matrices and self-duality conditions.