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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.
In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can determine the dimensions of their Euclidean hulls or Hermitian hulls. It turns out tha
The parameters of MDS self-dual codes are completely determined by the code length. In this paper, we utilize generalized Reed-Solomon (GRS) codes and extended GRS codes to construct MDS self-dual (self-orthogonal) codes and MDS almost self-dual code
In this paper, we propose a mechanism on the constructions of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon(GRS) codes with assigned dimensions of Euclidean hulls from self-orthogo
In this paper, we explore some properties of Galois hulls of cyclic serial codes over a chain ring and we devise an algorithm for computing all the possible parameters of the Euclidean hulls of that codes. We also establish the average $p^r$-dimensio
Given a commutative ring $R$ with identity, a matrix $Ain M_{stimes l}(R)$, and $R$-linear codes $mathcal{C}_1, dots, mathcal{C}_s$ of the same length, this article considers the hull of the matrix-product codes $[mathcal{C}_1 dots mathcal{C}_s],A$.