280 research outputs found
Constructions of optimal LCD codes over large finite fields
In this paper, we prove existence of optimal complementary dual codes (LCD
codes) over large finite fields. We also give methods to generate orthogonal
matrices over finite fields and then apply them to construct LCD codes.
Construction methods include random sampling in the orthogonal group, code
extension, matrix product codes and projection over a self-dual basis.Comment: This paper was presented in part at the International Conference on
Coding, Cryptography and Related Topics April 7-10, 2017, Shandong, Chin
Hulls of special typed linear codes and constructions of new EAQECCs
In this paper, we study Euclidean and Hermitian hulls of generalized
Reed-Solomon codes and twisted generalized Reed-Solomon codes, as well as the
Hermitian hulls of Roth-Lempel typed codes. We present explicit constructions
of MDS and AMDS linear codes for which their hull dimensions are well
determined. As an application, we provide several classes of
entanglement-assisted quantum error correcting codes with new parameters.Comment: 13 page
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