New Quantum MDS Code from Constacyclic Codes

In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable （MDS for short） codes from constacyclic MDS codes through the Hermitian construction. In this paper, a new class of quantum MDS code is constructed, which extends the result of [Theor...

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Bibliographic Details
Published inChinese annals of mathematics. Serie B Vol. 37; no. 6; pp. 891 - 898
Main Authors Hu, Liqin, Yue, Qin, Zhu, Xiaomeng
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2016
Springer Nature B.V
School of Communication Engineering,Hangzhou Dianzi University,Hangzhou 310018,China%Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China
Subjects
Applications of Mathematics
Codes
Mathematics
Mathematics and Statistics
Quantum MDS code
81P45
Cyclotomic coset
94B05
BCH bound
94B65
11T22
Constacyclic code
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Summary:In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable （MDS for short） codes from constacyclic MDS codes through the Hermitian construction. In this paper, a new class of quantum MDS code is constructed, which extends the result of [Theorems 3.14-3.15, Kai, X., Zhu, S., and Li, P., IEEE Trans. on Inf. Theory, 60（4）, 2014, 2080-2086], in the sense that our quantum MDS code has bigger minimum distance.
Bibliography:In recent years, there have been intensive activities in the area of constructing quantum maximum distance separable （MDS for short） codes from constacyclic MDS codes through the Hermitian construction. In this paper, a new class of quantum MDS code is constructed, which extends the result of [Theorems 3.14-3.15, Kai, X., Zhu, S., and Li, P., IEEE Trans. on Inf. Theory, 60（4）, 2014, 2080-2086], in the sense that our quantum MDS code has bigger minimum distance.
Cyclotomic coset, Quantum MDS code, Constacyclic code, BCH bound
31-1329/O1
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-016-1043-8