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Title: Xing–Ling codes, duals of their subcodes, and good asymmetric quantum codes
Authors: Ezerman, Martianus Frederic
Jitman, Somphong
Solé, Patrick
Keywords: Asymmetric Quantum Codes
CSS Codes
Issue Date: 2013
Source: Ezerman, M. F., Jitman, S., & Solé, P. (2015). Xing–Ling codes, duals of their subcodes, and good asymmetric quantum codes. Designs, Codes and Cryptography, 75(1), 21-42. doi:10.1007/s10623-013-9885-5
Series/Report no.: Designs, Codes and Cryptography
Abstract: A class of powerful q-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are q-ary block codes that encode k qudits of quantum information into n qudits and correct up to (dx − 1)/2 bit-flip errors and up to (dz − 1)/2 phase-flip errors. In many cases where the length (q2 − q)/2 ≤ n ≤ (q2 + q)/2 and the field size q are fixed and for chosen values of dx ∈ {2, 3, 4, 5} and dz ≥ δ, where δ is the designed distance of the Xing–Ling (XL) codes, the derived pure q-ary asymmetric quantum CSS codes possess the best possible size given the current state of the art knowledge on the best classical linear block codes.
ISSN: 0925-1022
Rights: © 2013 Springer Science+Business Media New York. All rights reserved. This paper was published in Designs, Codes and Cryptography and is made available with permission of Springer Science+Business Media New York.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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