Quantum CSS Duadic and Triadic Codes: New Insights and Properties
Reza Dastbasteh, Olatz Sanz Larrarte, Josu Etxezarreta Martinez,, Antonio deMarti iOlius, Javier Oliva del Moral, and Pedro Crespo Bofill
TL;DR
This paper introduces new quantum CSS duadic and triadic codes, providing methods for their construction, extension, and analysis of their minimum distances, advancing quantum error correction techniques.
Contribution
It presents novel construction methods for quantum CSS duadic and triadic codes, including extension techniques and distance bounds, with a focus on codes with larger dimensions and specific rates.
Findings
Extended quantum duadic codes with larger dimensions
Methods for estimating minimum distances of constructed codes
Introduction of quantum CSS triadic codes with rate at least 1/3
Abstract
In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum duadic codes. Furthermore, we present a technique for computing or bounding the minimum distances of quantum codes constructed through this approach. Additionally, we introduce quantum CSS triadic codes, a family of quantum codes with a rate of at least .
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Coding theory and cryptography