Quantum codes from cyclic codes over GF(4^m)

2000/08/30 by Andrew Thangaraj, Stephen McLaughlin, Thangaraj, Andrew +2
Computer Science · Physics and Astronomy · #Coding theory and cryptography #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0008129

7 pages, 0 figures, submitted to IEEE transactions on information theory

arxiv created 2000/08/30 · openalex publication_date 2000/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a construction for quantum codes (hermitian-self-orthogonal codes over GF(4)) starting from cyclic codes over GF(4^m). We also provide examples of these codes some of which meet the known bounds for quantum codes.

Related

• New quantum codes from self-dual codes over F₄
• Polynomial representation of additive cyclic codes and new quantum codes
• Elementary Constructions of Best Known Quantum Codes
• Quantum Error Correction via Codes over GF(4)
• Quasi-cyclic Hermitian construction of binary quantum codes