Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs

Xuefei Wu; Qi Liu; Yingchun Chen; Haiyan Zhou

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arXiv · 2609.20453

Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs

Xuefei Wu·Qi Liu·Yingchun Chen·Haiyan Zhou

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Abstract

The dimension of a Galois hull is an important parameter in the construction of entanglement-assisted quantum error-correcting codes. In this paper, we study generalized Roth-Lempel (GRL) codes with prescribed Galois hull dimensions over finite fields of arbitrary characteristic. We develop a common construction method based on normalized Lagrange coefficients and suitable choices of column multipliers, and obtain six explicit constructions from multiplicative cosets, trace fibers, additive-subspace cosets, and mixed additive--multiplicative fibers. For extension sizes $s=2$ and $s=3$, we construct MDS and AMDS GRL codes with Galois hulls of specific dimensions. The resulting codes provide EAQECCs with explicit dimension, entanglement consumption, and relatively large minimum distance. Taking zero-dimensional hulls also gives Hermitian LCD GRL codes and the corresponding maximally entangled EAQECCs.

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Xuefei Wu, Qi Liu, Yingchun Chen, Haiyan Zhou. 2026-09-17. Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs. https://arxiv.org/abs/2609.20453

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