A study of QECCs and EAQECCs construction from cyclic codes over the ring Fq+v1Fq+v2Fq+<middle dot><middle dot><middle dot>+vsFq

被引：0

作者：

Pandey, Om Prakash ^{[1
]}

Pathak, Sachin ^{[2
]}

Shukla, Awadhesh Kumar ^{[1
]}

Mishra, Vipul ^{[1
]}

Upadhyay, Ashish Kumar ^{[1
]}

机构：

[1] Banaras Hindu Univ, Dept Math, Varanasi 221005, Uttar Pradesh, India

[2] NIIT Univ, Dept Math & Basic Sci, Neemrana 301705, India

来源：

QUANTUM INFORMATION PROCESSING | 2024年 / 23卷 / 02期

关键词：

Cyclic codes; Generator polynomials; Euclidean sums and hulls of cyclic codes; QECCs and EAQECCs; QUANTUM CODES; CONSTACYCLIC CODES; MDS CODES;

D O I：

10.1007/s11128-023-04240-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we present a construction of quantum error-correcting codes (QECCs) codes and entanglement-assisted quantum error-correcting (EAQECCs) using Euclidean hulls and sums of cyclic codes of length n over a family of ring R-s=F-q+v(1)F(q)+v(2)Fq+<middle dot><middle dot><middle dot>+v(s)F(q )where q is an odd prime power and v(i)(2)=v(i), vivj=vjvi=0, for i,j=1,2,3,& ctdot;,s and i not equal j. The study delves into various aspects of this construction. We explore the generator polynomials, the dimension of both Euclidean hulls and the sums of cyclic codes over the ring R-s. Further, we determine several new QECCs and EAQECCs. This paper claims that our obtained codes have improved parameters (e.g. higher minimum distance or greater dimension) than the existing quantum codes. Moreover, we present some detailed examples that effectively illustrate our findings.

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页数：20

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