Complete Weight Distributions and MacWilliams Identities for Asymmetric Quantum Codes

Chuangqiang Hu; Shudi Yang; Stephen S.-T. Yau

doi:10.1109/ACCESS.2019.2918529

IEEE Access (Jan 2019)

Complete Weight Distributions and MacWilliams Identities for Asymmetric Quantum Codes

Chuangqiang Hu,
Shudi Yang,
Stephen S.-T. Yau

Affiliations

Chuangqiang Hu: Yau Mathematical Sciences Center, Tsinghua University, Beijing, China
Shudi Yang: School of Mathematical Sciences, Qufu Normal University, Shandong, China
Stephen S.-T. Yau: ORCiD; Department of Mathematical Sciences, Tsinghua University, Beijing, China

DOI: https://doi.org/10.1109/ACCESS.2019.2918529
Journal volume & issue: Vol. 7
pp. 68404 – 68414

Abstract

Read online

In 1997, Shor and Laflamme defined the weight enumerators for quantum error-correcting codes and derived a MacWilliams identity. We extend their work by introducing our double weight enumerators and complete weight enumerators for qubit codes and then investigate the MacWilliams identities for these enumerators. Based on the generalized MacWilliams identities, we solve an open problem, namely, the Singleton-type bound for asymmetric quantum codes (AQCs). Besides, the Hamming-type and the first linear-programming-type bounds for the AQCs are deduced similarly.

Published in IEEE Access

ISSN: 2169-3536 (Online)
Publisher: IEEE
Country of publisher: United States
LCC subjects: Technology: Electrical engineering. Electronics. Nuclear engineering
Website: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639

About the journal

Abstract

Keywords