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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{wu2026galois,
  title = {{Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs}},
  author = {Xuefei Wu and Qi Liu and Yingchun Chen and Haiyan Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20453},
  eprint = {2609.20453},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20453},
}
RIS
TY  - UNPB
TI  - Galois Hulls of Generalized Roth-Lempel Codes and Their Applications to EAQECCs
AU  - Xuefei Wu
AU  - Qi Liu
AU  - Yingchun Chen
AU  - Haiyan Zhou
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20453
UR  - https://arxiv.org/abs/2609.20453
AB  - 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.
ER  -