MDS codes with arbitrary dimensional hull and their applications

Gaojun Luo; Xiwang Cao

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arXiv · 1807.03166

MDS codes with arbitrary dimensional hull and their applications

Gaojun Luo·Xiwang Cao

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Abstract

The hull of linear codes have promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields with respect to the Euclidean inner product. Several infinite families of MDS codes with arbitrary dimensional hull are presented. As an application, using these MDS codes with arbitrary dimensional hull, we construct several new infinite families of entanglement-assisted quantum error-correcting codes with flexible parameters.

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Gaojun Luo, Xiwang Cao. 2018-07-06. MDS codes with arbitrary dimensional hull and their applications. https://arxiv.org/abs/1807.03166

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