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

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.