Abstract
In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian function field. 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. Furthermore, a number of the new codes meet or even exceed the quantum Gilbert–Varshamov bound.
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The authors wish to thank the anonymous reviewers for their thorough reading of the manuscript and their valuable suggestions.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Codes, Cryptology and Curves”.
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Christensen, R.B., Geil, O. Steane-enlargement of quantum codes from the Hermitian function field. Des. Codes Cryptogr. 88, 1639–1652 (2020). https://doi.org/10.1007/s10623-019-00709-7
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DOI: https://doi.org/10.1007/s10623-019-00709-7