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Published in: Applicable Algebra in Engineering, Communication and Computing 3/2022

27-06-2020 | Original Paper

Quantum BCH codes with maximum designed distance

Authors: Xinmei Huang, Qin Yue, Xiaoping Shi, Yiwei Huang

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 3/2022

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Abstract

In this paper, we investigate all coset leaders of primitive BCH codes for \(\delta\) in the range \(1\le \delta \le q^\frac{m+7}{2}\), which extends Liu and Shi’s results. Besides, we also generalize Shi’s results by proposing the maximum designed distance of non-narrow-sense(\(b=k_2q^2+k_1q+k_0\)) primitive BCH codes which can contain their Euclidean dual. At the end, we calculate the dimension of the Euclidean dual containing non-narrow-sense primitive BCH codes and construct some quantum BCH codes.
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Metadata
Title
Quantum BCH codes with maximum designed distance
Authors
Xinmei Huang
Qin Yue
Xiaoping Shi
Yiwei Huang
Publication date
27-06-2020
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 3/2022
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-020-00443-x

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