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Fp-Linear and Fpm-Linear Qudit Codes From Dual-Containing Classical Codes

Nadkarni, PJ and Garani, SS (2021) Fp-Linear and Fpm-Linear Qudit Codes From Dual-Containing Classical Codes. In: IEEE Transactions on Quantum Engineering, 2 .

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Official URL: https://doi.org/10.1109/TQE.2021.3078152


Quantum code construction from two classical codes D1[n, k1, d1] and D2[n, k2, d2] over the field Fpm (p is prime and m is an integer) satisfying the dual containing criteria D⊥1 ⊂ D2 using the Calderbank-Shor-Steane (CSS) framework is well-studied. We show that the generalization of the CSS framework for qubits to qudits yields two different classes of codes, namely, the Fp-linear CSS codes and the well-known Fpm-linear CSS codes based on the check matrix-based definition and the coset-based definition of CSS codes over qubits. Our contribution to this article are three-folds. 1) We study the properties of the Fp-linear and Fpm-linear CSS codes and demonstrate the tradeoff for designing codes with higher rates or better error detection and correction capability, useful for quantum systems. 2) For Fpm-linear CSS codes, we provide the explicit form of the check matrix and show that the minimum distances dx and dz are equal to d2 and d1, respectively, if and only if the code is nondegenerate. 3) We propose two classes of quantum codes obtained from the codes D1 and D2, where one code is an Fpl-linear code (l divides m) and the other code is obtained from a particular subgroup of the stabilizer group of the Fpm-linear CSS code. Within each class of codes, we demonstrate the tradeoff between higher rates and better error detection and correction capability.

Item Type: Journal Article
Publication: IEEE Transactions on Quantum Engineering
Publisher: Institute of Electrical and Electronics Engineers Inc.
Additional Information: The copyright for this article belongs to the Authors(s).
Keywords: Error correction; Error detection; Matrix algebra; Quantum optics, Calderbank-Shor-Steane codes; Calderbank-shor-steane-like code; Classes of codes; Dual containing code; Fpm-linear calderbank-shor-steane code; Fpm-linear calderbank-shor-steane code; Quantum codes; Quantum error corrections; Qudit code, Qubits
Department/Centre: Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Date Deposited: 15 Nov 2022 07:05
Last Modified: 15 Nov 2022 07:05
URI: https://eprints.iisc.ac.in/id/eprint/77928

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