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Quantum codes from two-point Hermitian codes

Justine C. Hyde-Volpe

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

We explore the background on error-correcting codes, including linear codes and quantum codes from curves. Then we consider the parameters of quantum codes constructed from two-point Hermitian codes.

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A curve attaining the Hasse-Weil bound is called a maximal curve. Usually, classical error-correcting codes obtained from a maximal curve have good parameters. However, the quantum stabilizer codes obtained from such classical error-correcting codes via Euclidean or Hermitian self-orthogonality do not always possess good parameters. In this paper, the Hermitian self-orthogonality of algebraic geometry codes obtained from two maximal curves is investigated. It turns out that the stabilizer quantum codes produced from such Hermitian self-orthogonal classical codes have good parameters.