Steane enlargement of Cartesian-product codes is proven to add at least K quantum dimensions, with an algorithm giving the exact gain, and several resulting codes meet or beat the Gilbert-Varshamov bound.
Steane-Enlargement of Quantum Codes from the Hermitian Curve
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In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In particular, the paper contains two constructions of quantum codes whose parameters are described by explicit formulae, and we show that these codes compare favourably to existing, comparable constructions in the literature.
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On Steane-Enlargement of Quantum Codes from Cartesian Product Point Sets
Steane enlargement of Cartesian-product codes is proven to add at least K quantum dimensions, with an algorithm giving the exact gain, and several resulting codes meet or beat the Gilbert-Varshamov bound.