🤖 AI Summary
本文研究了一类扭曲的Roth-Lempel码，探讨了其最小距离、MDS和NMDS性质，并证明了这些码不同于传统的Roth-Lempel码。
📝 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.