Quantum Goethals-Preparata Codes
Markus Grassl, Martin Roetteler

TL;DR
This paper introduces a new family of non-additive quantum codes derived from classical Goethals and Preparata codes, achieving significantly higher dimensions than existing additive quantum codes with the same length and minimum distance.
Contribution
It presents a novel construction of non-additive quantum codes based on classical codes, with improved dimension over known additive quantum codes.
Findings
Codes have parameters ((2^m,2^{2^m-5m+1},8))
Dimension is eight times higher than best known additive codes
Achieves the same minimum distance with larger code dimension
Abstract
We present a family of non-additive quantum codes based on Goethals and Preparata codes with parameters ((2^m,2^{2^m-5m+1},8)). The dimension of these codes is eight times higher than the dimension of the best known additive quantum codes of equal length and minimum distance.
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