Some families of optimal quantum codes derived from constacyclic codes. Issue 4 (3rd April 2019)

• Record Type: Journal Article
• Authors: Chen, Jianzhang; Huang, Yuanyuan; Feng, Chunhui; Chen, Riqing
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 4(2019)
• Page Start: 725
• Page End: 742
• Publication Date: 2019-04-03
• Subjects: Asymmetric quantum codes -- constacyclic codes -- quantum convolutional codes -- quantum Singleton bound; 81P45 -- 81P70; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1432544
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: Quantum maximum-distance-separable (MDS) codes form an important family of quantum codes. Quantum MDS codes are optimal, which can attain the quantum Singleton bound. In this paper, using some classes of constacyclic codes and Hermitian constructions, we propose the constructions of optimal quantum convolutional codes and optimal asymmetric quantum codes in the sense of the quantum Singleton bound. Compared with the codes obtained in the literature, the parameters of the constructed quantum codes are new as well as the distanced z of optimal asymmetric quantum codes[ [ n, k, d z / d x ] ] q 2 constructed in this paper is larger.