2025/02/07 by Hu Zhao, Liang Wang, Hu, Zhao +7
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Rings, Modules, and Algebras #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2502.04746
openalex publication_date 2025/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Twisted generalized Reed-Solomon (TGRS) codes are an extension of the generalized Reed-Solomon (GRS) codes by adding specific twists, which attract much attention recently. This paper presents an in-depth and comprehensive investigation of the TGRS codes for the most general form by using a universal method. At first, we propose a more precise definition to describe TGRS codes, namely (L,P)-TGRS codes, and provide a concise necessary and sufficient condition for (L,P)-TGRS codes to be MDS, which extends the related results in the previous works. Secondly, we explicitly characterize the parity check matrices of (L,P)-TGRS codes, and provide a sufficient condition for (L,P)-TGRS codes to be self-dual. Finally, we conduct an in-depth study into the non-GRS property of (L,P)-TGRS codes via the Schur squares and the combinatorial techniques respectively. As a result, we obtain a large infinite families of non-GRS MDS codes.