Quantum mechanics

Algorithm

Engineering

Discrete mathematics

Probability of error

Marine engineering

Quantum convolutional code

Reed–Muller code

Computer science

Decoding methods

Physics

Quantum entanglement

Coding theory

Mathematics

Hull

Reed–Solomon error correction

Block code

Geometry

Concatenated error correction code

Quantum

Combinatorics

Error detection and correction

Euclidean geometry

Linear code

Arithmetic

IEEE Transactions on Information Theory

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.

MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction