Two classes of LCD codes derived from $(mathcal{L},mathcal{P})$-TGRS codes
arXiv:2601.16438v1 Announce Type: new
Abstract: Twisted generalized Reed-Solomon (TGRS) codes, as a flexible extension of classical generalized Reed-Solomon (GRS) codes, have attracted significant attention in recent years. In this paper, we construct two classes of LCD codes from the $(mathcal{L},mathcal{P})$-TGRS code $mathcal{C}_h$ of length $n$ and dimension $k$, where $mathcal{L}={0,1,ldots,l}$ for $lleq n-k-1$ and $mathcal{P}={h}$ for $1leq hleq k-1$. First, we derive the parity check matrix of $mathcal{C}_h$ and provide a necessary and sufficient condition for $mathcal{C}_h$ to be an AMDS code. Then, we construct two classes of LCD codes from $mathcal{C}_h$ by suitably choosing the evaluation points together with certain restrictions on the coefficient of $x^{h-1}$ in the polynomial associated with the twisting term. From the constructed LCD codes we further obtain two classes of LCD MDS codes. Finally, several examples are presented.
