Optimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length $3p^s$ Optimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length $$3p^s$$

Hai Quang Dinh, Bac Trong Nguyen, M. Paravee +2 more

Quantum Information ProcessingJun 24, 20234 citations

Non-Binary Quantum Synchronizable Codes From Repeated-Root Cyclic Codes

Lan Luo, Zhi Ma

In this paper, we construct a new family of quantum synchronizable codes from repeated-root cyclic codes of lengths psand lpsover Fq, where s 1 andl ≥ 2 are integers, and p ≥ 3 is the odd characteristic. Within some loose limitations, these synchronizable codes can possess the best possible capability in synchronization recovery, and therefore, enriches the variety of good quantum synchronizable codes. Furthermore, by using known techniques in classical coding theory which convert the computation of the minimum distance of a repeated-root cyclic code to that of a shorter simple-root cyclic code, we prove that the repeated-root cyclic codes of lengths ps and l ps are in general better than narrow-sense BCH codes of close lengths in terms of minimum distances, and thereby enable the obtained synchronizable codes to correct more Pauli errors.In this paper, we construct a new family of quantum synchronizable codes from repeated-root cyclic codes of lengths psand lpsover Fq, where s 1 andl ≥ 2 are integers, and p ≥ 3 is the odd characteristic. Within some loose limitations, these synchronizable codes can possess the best possible capability in synchronization recovery, and therefore, enriches the variety of good quantum synchronizable codes. Furthermore, by using known techniques in classical coding theory which convert the computation of the minimum distance of a repeated-root cyclic code to that of a shorter simple-root cyclic code, we prove that the repeated-root cyclic codes of lengths ps and l ps are in general better than narrow-sense BCH codes of close lengths in terms of minimum distances, and thereby enable the obtained synchronizable codes to correct more Pauli errors.

IEEE Transactions on Information TheoryJan 19, 201835 citations

Quantum Codes Derived from Cyclic Codes

Giuliano G. La Guardia

arXiv:1705.00239International Journal of Theoretical PhysicsApr 29, 201734 citations

Algebraic quantum synchronizable codes

Kenza Guenda, Giuliano G. La Guardia, Thomas Aaron Gulliver

arXiv:1508.05977Journal of Applied Mathematics and ComputingSep 20, 201610 citations

On a Family of Quantum Synchronizable Codes Based on the $(\lambda(u + v)|u - v)$ ConstructionOn a Family of Quantum Synchronizable Codes Based on the $(\lambda(u + v)|u - v)$ Construction

Chao Du, Zhi Ma, Lan Luo +2 more

In this paper, we propose a family of quantum synchronizable codes from repeated-root cyclic codes and constacyclic codes. This family of quantum synchronizable codes are based on (λ(u + v)|u - v) construction which is constructed from constacyclic codes. Under this construction, we enrich the varieties of valid quantum synchronizable codes. We also prove that the obtained quantum synchronizable codes can achieve maximum synchronization error tolerance. Furthermore, quantum synchronizable codes based on (λ(u + v)|u - v) construction are shown to be able to have a better capability in correcting bit errors than those from projective geometry codes.In this paper, we propose a family of quantum synchronizable codes from repeated-root cyclic codes and constacyclic codes. This family of quantum synchronizable codes are based on (λ(u + v)|u - v) construction which is constructed from constacyclic codes. Under this construction, we enrich the varieties of valid quantum synchronizable codes. We also prove that the obtained quantum synchronizable codes can achieve maximum synchronization error tolerance. Furthermore, quantum synchronizable codes based on (λ(u + v)|u - v) construction are shown to be able to have a better capability in correcting bit errors than those from projective geometry codes.

IEEE AccessDec 31, 20196 citations

Optimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length

3p^s

On a Family of Quantum Synchronizable Codes Based on the

(\lambda(u + v)|u - v)

Construction