QEC and EAQEC Codes from Hermitian Sums and Hulls of Cyclic Codes over $\mathbb{F}_2 \times (\mathbb{F}_2+v\mathbb{F}_2)$
The paper provides a theoretical construction method for QEC and EAQEC codes from cyclic codes over a composite ring, which is incremental for coding theory researchers.
This work determines generator polynomials for Hermitian hulls and sums of cyclic codes over a specific composite ring, and uses them to construct quantum error-correcting (QEC) codes and entanglement-assisted quantum error-correcting (EAQEC) codes. No concrete numerical results are reported.
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.