Duadic Group Algebra Codes
Salah A. Aly, Andreas Klappenecker, Pradeep Kiran Sarvepalli
TL;DR
This paper proves the existence of duadic group algebra codes, a generalization of quadratic residue codes, and explores their application in constructing quantum stabilizer codes with improved error correction properties.
Contribution
It resolves an open problem about the existence of duadic group algebra codes and demonstrates their use in quantum error correction.
Findings
Existence of duadic group algebra codes established
Application in constructing degenerate quantum stabilizer codes
Example illustrating error correction advantages
Abstract
Duadic group algebra codes are a generalization of quadratic residue codes. This paper settles an open problem raised by Zhu concerning the existence of duadic group algebra codes. These codes can be used to construct degenerate quantum stabilizer codes that have the nice feature that many errors of small weight do not need error correction; this fact is illustrated by an example.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Coding theory and cryptography