Skew G-codes over $\mathbb {F}_4[u,v]/\langle u^2, v^2, uv-vu \rangle $ and new binary entanglement-assisted quantum error-correcting codes

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2025年6月27日

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Serap Şahinkaya,
Deniz Ustun

摘要

In this paper, we explore the algebraic structure of skew-G codes over the ring $A= \mathbb {F}_4[u,v]/\langle u^2, v^2, uv - vu \rangle $ $A = F_{4} [u, v] / ⟨ u^{2}, v^{2}, u v - v u ⟩$ . In addition to that, we bridge theoretical results with practical applications in quantum computing. More specifically, we derive a significant number of new binary EAQEC codes from the gray images of the skew-G codes over A according to Grassl’s codetable [14].

Skew G-codes over \(\mathbb {F}_4[u,v]/\langle u^2, v^2, uv-vu \rangle \) and new binary entanglement-assisted quantum error-correcting codes

摘要