Column Twisted Reed-Solomon Codes as MDS Codes
For coding theorists, this provides a new method to construct MDS codes with more flexible parameters, though the improvement is incremental.
This paper studies column twisted Reed-Solomon codes and establishes sufficient conditions for them to be MDS. The construction supports code lengths up to (q+3)/2 for odd prime power q, improving over existing twisted generalized Reed-Solomon codes limited to (q+1)/2.
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.