Generalized extended codes are shown to be monomially equivalent to certain Hermitian duals, with explicit criteria for controlling Hermitian hull dimension and dual distance, yielding 267 new EA qubit codes and 14 new EA qutrit codes with improved parameters.
QEC and EAQEC Codes from Hermitian Sums and Hulls of Cyclic Codes over $\mathbb{F}_2 \times (\mathbb{F}_2+v\mathbb{F}_2)$
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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.
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2026 1verdicts
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Generalized Extended Codes with Applications in Entanglement-Assisted Qubit and Qutrit Codes
Generalized extended codes are shown to be monomially equivalent to certain Hermitian duals, with explicit criteria for controlling Hermitian hull dimension and dual distance, yielding 267 new EA qubit codes and 14 new EA qutrit codes with improved parameters.