Hulls of special typed linear codes and constructions of new EAQECCs
Lin Sok
TL;DR
This paper investigates the hull structures of various linear codes, providing explicit constructions and applying these to develop new entanglement-assisted quantum error correcting codes with improved parameters.
Contribution
It introduces explicit constructions of linear codes with known hull dimensions and applies them to generate novel EAQECCs with better parameters than existing codes.
Findings
Constructed MDS and AMDS codes with specified hull dimensions.
Derived new EAQECCs with improved parameters.
Analyzed hulls of Reed-Solomon and Roth-Lempel codes.
Abstract
In this paper, we study Euclidean and Hermitian hulls of generalized Reed-Solomon codes and twisted generalized Reed-Solomon codes, as well as the Hermitian hulls of Roth-Lempel typed codes. We present explicit constructions of MDS and AMDS linear codes for which their hull dimensions are well determined. As an application, we provide several classes of entanglement-assisted quantum error correcting codes with new parameters.
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Taxonomy
TopicsCoding theory and cryptography · Quantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata