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PreprintarXiv licencearXiv

On Twisted Roth-Lempel Codes

  • Huiyue Lei
  • Haojie Gu
  • Jun Zhang
  • Haiyan Zhou
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Abstract

In 1989, Roth and Lempel constructed a well-known family of non-Reed-Solomon maximum distance separable (MDS) codes. For decades, this family of codes has attracted extensive research attention due to its algebraic structure, low-complexity decoding, and broad applications in cryptography and data storage. In this paper, we present a class of twisted Roth-Lempel codes. We investigate their minimum distance, MDS and NMDS properties. Specifically, we determine the necessary and sufficient conditions for the TRL codes to have minimum distance n-k or n-k+1. Furthermore, we determine the necessary and sufficient conditions for the TRL code to be an MDS or NMDS code. Moreover, we show that the dimension of the Schur square of the TRL code is at least 2k+1, and thus the TRL code is a non-RS code inequivalent to the corresponding RL code.

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Cite

BibTeXRIS
BibTeX
@misc{lei2026twisted,
  title = {{On Twisted Roth-Lempel Codes}},
  author = {Huiyue Lei and Haojie Gu and Jun Zhang and Haiyan Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17304},
  eprint = {2609.17304},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17304},
}
RIS
TY  - UNPB
TI  - On Twisted Roth-Lempel Codes
AU  - Huiyue Lei
AU  - Haojie Gu
AU  - Jun Zhang
AU  - Haiyan Zhou
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17304
UR  - https://arxiv.org/abs/2609.17304
AB  - In 1989, Roth and Lempel constructed a well-known family of non-Reed-Solomon maximum distance separable (MDS) codes. For decades, this family of codes has attracted extensive research attention due to its algebraic structure, low-complexity decoding, and broad applications in cryptography and data storage. In this paper, we present a class of twisted Roth-Lempel codes. We investigate their minimum distance, MDS and NMDS properties. Specifically, we determine the necessary and sufficient conditions for the TRL codes to have minimum distance n-k or n-k+1. Furthermore, we determine the necessary and sufficient conditions for the TRL code to be an MDS or NMDS code. Moreover, we show that the dimension of the Schur square of the TRL code is at least 2k+1, and thus the TRL code is a non-RS code inequivalent to the corresponding RL code.
ER  -