MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction
Gaojun Luo, Xiwang Cao, Xiaojing Chen · IEEE Transactions on Information Theory · 2018
The hull of linear codes has 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 hulls of arbitrary dimensions are presented. As an application, using these MDS codes with hulls of arbitrary dimensions, we construct several new infinite families of entanglement-assisted quantum error-correcting codes with flexible parameters.