New Galois Hulls of GRS Codes and Application to EAQECCs
Xiaolei Fang, Renjie Jin, Jinquan Luo, Wen Ma
TL;DR
This paper introduces new classes of Galois hulls of GRS codes with arbitrary dimensions and applies these to construct novel entanglement-assisted quantum error-correcting codes, enhancing quantum coding theory.
Contribution
It presents a general method for constructing GRS codes with Galois hulls of arbitrary dimensions and develops new EAQECCs based on these codes.
Findings
Constructed GRS codes with Galois hulls of arbitrary dimensions.
Developed a method from Euclidean orthogonal GRS codes.
Created new families of EAQECCs and MDS EAQECCs.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCoding theory and cryptography · Quantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata