New QEC codes and EAQEC codes from repeated-root cyclic codes of length 2^rp^s

2024/06/20 by Lanqiang Li, Li, Lanqiang, Ziwen Cao +5
Computer Science · #11T71(Secondary) #94B15 (Primary) 94B05 #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.2406.13943

openalex publication_date 2024/06/20 · openalex created_date 2024/06/22 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime and r,s,m be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of 2^rp^s over the finite field \mathbbF_p^m. Through the utilization of CSS and Steane's constructions, a series of new quantum error-correcting (QEC) codes are constructed with parameters distinct from all previous constructions. Furthermore, we provide all maximum distance separable (MDS) cyclic codes of length 2^rp^s, which are further utilized in the construction of QEC MDS codes. Finally, we introduce a significant number of novel entanglement-assisted quantum error-correcting (EAQEC) codes derived from these repeated-root cyclic codes. Notably, these newly constructed codes exhibit parameters distinct from those of previously known constructions.

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