We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Two families of BCH codes and new quantum codes.
- Authors
Song, Hao; Li, Ruihu; Wang, Junli; Liu, Yang
- Abstract
In this paper, two families of non-narrow-sense (NNS) BCH codes of lengths n=q2m-1q2-1<inline-graphic></inline-graphic> and n=q2m-1q+1<inline-graphic></inline-graphic> (m≥3)<inline-graphic></inline-graphic> over the finite field Fq2<inline-graphic></inline-graphic> are studied. The maximum designed distances δmaxnew<inline-graphic></inline-graphic> of these dual-containing BCH codes are determined by a careful analysis of properties of the cyclotomic cosets. NNS BCH codes which achieve these maximum designed distances are presented, and a sequence of nested NNS BCH codes that contain these BCH codes with maximum designed distances are constructed and their parameters are computed. Consequently, new nonbinary quantum BCH codes are derived from these NNS BCH codes. The new quantum codes presented here include many classes of good quantum codes, which have parameters better than those constructed from narrow-sense BCH codes, negacyclic and constacyclic BCH codes in the literature.
- Subjects
BCH codes; QUANTUM error correcting codes; QUANTUM computing; CYCLOTOMY; FINITE fields
- Publication
Quantum Information Processing, 2018, Vol 17, Issue 10, p1
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-018-2042-3