Quantum codes from Hermitian dual-containing cyclic codes. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Mi, Jiafu; Cao, Xiwang; Xu, Shanding; Luo, Gaojun
• Is Part Of: International journal of computer mathematics. Volume 2:Issue 3(2017)
• Page Start: 97
• Page End: 109
• Publication Date: 2017-07-03
• Subjects: Quantum MDS codes -- cyclotomic cosets -- dual-containing -- cyclic codes -- existence conditions; 11T71 -- 94B15; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2017.1330284
• Languages: English
• ISSNs: 2379-9927

Abstract

ABSTRACT: A new criterion for the existence of Hermitian dual-containing cyclic codes is obtained based on a characterization of q -cyclotomic cosets modulo n . This criterion admits a method of constructing new Hermitian dual-containing cyclic codes (hence new quantum codes) from the old ones, and enables us to construct several classes of quantum maximum-distance-separable (MDS) codes from classical Hermitian dual-containing cyclic codes. We analyse that our codes are good in certain sense. Besides, some enumerative conclusions are also presented as a result of the characterization of q -cyclotomic cosets modulo n .