Non-Additive Quantum Codes from Goethals and Preparata Codes
Markus Grassl, Martin Roetteler
TL;DR
This paper introduces a method to construct non-additive quantum error-correcting codes from non-linear classical codes, specifically using Goethals and Preparata codes, expanding the quantum coding theory framework.
Contribution
It extends the stabilizer formalism to include non-additive codes derived from classical non-linear codes, providing new families of quantum codes.
Findings
Constructed infinite families of non-additive quantum codes
Demonstrated codes derived from Goethals and Preparata codes
Expanded the theoretical framework for quantum code construction
Abstract
We extend the stabilizer formalism to a class of non-additive quantum codes which are constructed from non-linear classical codes. As an example, we present infinite families of non-additive codes which are derived from Goethals and Preparata codes.
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