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- Title
Linear codes with arbitrary dimensional hull and their applications to EAQECCs.
- Authors
Sok, Lin; Qian, Gang
- Abstract
The Euclidean hull dimension of a linear code is an important quantity to determine the parameters of an entanglement-assisted quantum error-correcting code (EAQECC) if the Euclidean construction is applied. In this paper, we study the Euclidean hull of a linear code by means of orthogonal matrices. We provide some methods to construct linear codes over F p m with hull of arbitrary dimensions. With existence of self-dual bases of F p m over F p , we determine a Gray map from F p m to F p m , and from a given linear code over F p m with one-dimensional hull, we construct, using such a Gray map, a linear code over F p with m-dimensional hull for all m when p is even and for all m odd when p is odd. Comparisons with classical constructions are made, and some good EAQECCs over F q , q = 2 , 3 , 4 , 5 , 9 , 13 , 17 , 49 are presented.
- Subjects
ERROR-correcting codes; LINEAR codes; ORTHOGONAL codes; GRAY codes; TWO-dimensional bar codes; MATRIX multiplications; PRODUCT coding
- Publication
Quantum Information Processing, 2022, Vol 21, Issue 2, p1
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-021-03407-3