New families of additive non-RS MDS codes and ACD codes from twisted Reed-Solomon codes

@misc{li2026families,
  title = {{New families of additive non-RS MDS codes and ACD codes from twisted Reed-Solomon codes}},
  author = {Xia Li and Yu Wang and Yansheng Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35105},
  eprint = {2610.35105},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35105},
  note = {CC BY-NC-ND 4.0},
}

TY  - UNPB
TI  - New families of additive non-RS MDS codes and ACD codes from twisted Reed-Solomon codes
AU  - Xia Li
AU  - Yu Wang
AU  - Yansheng Wu
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35105
UR  - https://arxiv.org/abs/2610.35105
AB  - Additive codes generalize linear codes and play an important role in the construc?tion of quantum codes. As generalizations of linear MDS codes, additive MDS codes have received much research attention. As an important subclass of additive codes, ACD codes are widely used for quantum error correction. In this paper, we study single-twist additive generalized twisted Reed-Solomon (GTRS) codes over finite fields. We derive necessary and sufficient conditions for these codes to be MDS for arbitrary hook and twist parameters. Then we employ Schur squares to prove that such additive MDS codes are not monomially equivalent to additive Reed-Solomon codes. We also identify a class of additive GTRS codes whose duals remain additive GTRS codes, and show that, for all sufficiently large prime powers q whose characteristic avoids a finite set, such GTRS codes yield ACD codes.
ER  -