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International Symposium on Turbo Codes and Iterative Information Processing

Two Families of Entanglement-Assisted Quantum Codes from Algebraic Plane Curves

Lin Sok, San Ling

Published Aug 18, 2025• 1 citation
Publisher

Abstract

This article studies the Hermitian hulls of linear codes from algebraic plane curves of a special type. We provide lower bounds on the hull dimension of one-point algebraic geometry codes. We derive two families of entanglement-assisted quantum codes from one-point algebraic geometry codes, using the Hermitian approach.
DOI
10.1109/istc65386.2025.11154485

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Hermitian hulls of linear codes are interesting for theoretical and practical reasons alike. In terms of recent application, linear codes whose hulls meet certain conditions have been utilized as ingredients to construct entanglement-assisted quantum error correcting codes. This family of quantum codes is often seen as a generalization of quantum stabilizer codes. Theoretically, compared with the Euclidean setup, the Hermitian case is much harder to deal with. Hermitian hulls of MDS linear codes with low dimensions have been explored, mostly from generalized Reed-Solomon codes. Characterizing Hermitian hulls which themselves are MDS appears to be more involved and has not been extensively studied. This paper introduces some tools to study linear codes whose Hermitian hulls are MDS. Using the tools, we then propose explicit constructions of such codes. We consider Hermitian hulls of both Reed-Solomon and non Reed-Solomon types of linear MDS codes. We demonstrate that, given the same Hermitian hull dimensions, the codes from our constructions have dimensions which are larger than those in the literature.