Quantum Information Processing

Quantum codes construction from cyclic codes over matrix rings

Soham Ravikant Joshi, Shikha Patel, Om Prakash

Published Jun 9, 2026• 0 citations

DOI: 10.1007/s11128-026-05230-0

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Quantum Information Processing

Quantum codes construction from cyclic codes over matrix rings

Soham Ravikant Joshi, Shikha Patel, Om Prakash

Published Jun 9, 2026• 0 citations

Publisher

DOI: 10.1007/s11128-026-05230-0

Related papers

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

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.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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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.

For an odd prime power q and

{\mathcal{R}}_{7}=\mathbb{F}_{q}+u \mathbb{F}_{q}+

v \mathbb{F}_{q}+w \mathbb{F}_{q}+z \mathbb{F}_{q}+u^{2} \mathbb{F}_{q}+w z \mathbb{F}_{q}

. Through this work we seek to construct new quantum codes and LCD codes by means of cyclic codes built on the ring

{\mathcal{R}}_{7}

. By using cyclic codes containing their duals, we give quantum codes, we also give a method for the construction of LCD Codes over

{\mathcal{R}}_{7}