New Galois Hulls of GRS Codes and Application to EAQECCs

November 28, 2020 · Declared Dead · 🏛 Cryptography and Communications

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Authors Xiaolei Fang, Renjie Jin, Jinquan Luo, Wen Ma arXiv ID 2011.14061 Category cs.IT: Information Theory Citations 32 Venue Cryptography and Communications Last Checked 3 months ago
Abstract
Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a general method on constructing GRS codes with Galois hulls of arbitrary dimensions from special Euclidean orthogonal GRS codes. Finally, we construct several new families of entanglement-assisted quantum error-correcting codes (EAQECCs) and MDS EAQECCs by utilizing the above results.
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