Column Twisted Reed-Solomon Codes as MDS Codes

Abstract: In this paper, we study column twisted Reed-Solomon(TRS) codes. We establish some conditions for column TRS codes to be MDS codes and show that the dimension of their Schur square codes is $2k$. Consequently, these TRS codes are not equivalent to Reed-Solomon(RS) codes. Moreover, this construction method provides more flexible parameters compared to previous twisted generalized Reed-Solomon(TGRS) code constructions. For large odd prime power $q$, different from the systematically constructed TGRS codes whose length was previously limited to $\frac{q+1}{2}$, our construction achieves code lengths up to $\frac{q+3}{2}$. Finally, we present the dual codes of column TRS codes. This paper provides a new approach to construct MDS codes by adding column vectors to generator matrix of RS codes.