Additive codes with new structures help quantum error correction
New families of additive non-RS MDS codes and ACD codes from twisted Reed-Solomon codes
Information Theory
Summary
Error-correcting codes help protect information from mistakes during transmission or storage. This paper studies a special kind of code called additive generalized twisted Reed-Solomon codes, which are more general than many known codes. The authors found conditions making these codes optimal in terms of error correction and showed that they are different from previously known codes. They also identified a group of these codes useful for quantum error correction, improving tools for protecting quantum information.
What this means in practice
- •For quantum hardware engineers: Use new additive codes to build more reliable quantum error correction schemes for quantum computing devices.
- •For communications protocol designers: Design error correction methods with additive MDS codes that differ structurally from traditional Reed-Solomon codes for enhanced data integrity.
Authors
Xia Li, Yu Wang, Yansheng Wu
Abstract
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.