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• W2974676816 abstract "Hulls of linear codes have been of interest and extensively studied due to their rich algebraic structures and wide applications. In this paper, alternative characterizations of hulls of linear codes are given as well as their applications. Properties of hulls of linear codes are given in terms of their Gramians of their generator and parity-check matrices. Moreover, it is show that the Gramian of a generator matrix of every linear code over a finite field of odd characteristic is diagonalizable. Subsequently, it is shown that a linear code over a finite field of odd characteristic is complementary dual if and only if it has an orthogonal basis. Based on this characterization, constructions of good entanglement-assisted quantum error-correcting codes are provided." @default.
• W2974676816 created "2019-09-26" @default.
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• W2974676816 date "2019-09-18" @default.
• W2974676816 modified "2023-09-30" @default.
• W2974676816 title "Hulls of linear codes revisited with applications" @default.
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• W2974676816 doi "https://doi.org/10.1007/s12190-019-01286-7" @default.
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