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arXiv:2606.02137

QEC and EAQEC Codes from Hermitian Sums and Hulls of Cyclic Codes over $\mathbb{F}_2 \times (\mathbb{F}_2+v\mathbb{F}_2)$

Rabia Zengin, Mehmet E. Köroğlu

Published Jun 1, 2026• 0 citations
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Abstract

In this work, we determine the generator polynomials for the Hermitian hulls and Hermitian sums of cyclic codes defined over the composite ring $\mathbb{F}_2 \times (\mathbb{F}_2 + v\mathbb{F}_2)$, where $v^2 = v$. Based on these structures, we develop quantum error-correcting (QEC) codes by applying the Hermitian dual version of Quantum Construction~X to the obtained Hermitian hulls and sums. Moreover, by employing matrix product code methods on linear complementary dual (LCD) codes defined over the same ring, we derive families of entanglement-assisted quantum error-correcting (EAQEC) codes.

DOI
10.48550/arxiv.2606.02137

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QEC and EAQEC Codes from Hermitian Sums and Hulls of Cyclic Codes over F2×(F2+vF2)\mathbb{F}_2 \times (\mathbb{F}_2+v\mathbb{F}_2)F2​×(F2​+vF2​)
In this work, we determine the generator polynomials for the Hermitian hulls and Hermitian sums of cyclic codes defined over the composite ring F2×(F2+vF2)\mathbb{F}_2 \times (\mathbb{F}_2 + v\mathbb{F}_2)F2​×(F2​+vF2​), where v2=vv^2 = vv2=v. Based on these structures, we develop quantum error-correcting (QEC) codes by applying the Hermitian dual version of Quantum Construction~X to the obtained Hermitian hulls and sums. Moreover, by employing matrix product code methods on linear complementary dual (LCD) codes defined over the same ring, we derive families of entanglement-assisted quantum error-correcting (EAQEC) codes.
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