Twisted Roth-Lempel codes offer new error correction options
On Twisted Roth-Lempel Codes
Information Theory
Summary
Error correction codes help protect data from mistakes or losses. Roth and Lempel created a special type of such codes that many use in data storage and cryptography. This paper studies a new twist on those codes, called twisted Roth-Lempel (TRL) codes, and finds exact conditions when they work best. The authors also show these new codes differ from the old ones in important mathematical ways, which might help in applications needing strong, efficient error correction.
What this means in practice
- •For data storage engineers: Design storage systems with new code options that guarantee strong error correction and potential efficiency improvements.
- •For cryptography developers: Incorporate twisted Roth-Lempel codes to secure data transmissions using codes distinct from classical Reed-Solomon methods.
Authors
Huiyue Lei, Haojie Gu, Jun Zhang, Haiyan Zhou
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.