Optimal quaternary linear codes with one-dimensional Hermitian hull and the related EAQECCs
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Linear codes with small hulls over finite fields have been extensively studied due to their practical applications in computational complexity and information protection. In this paper, we develop a general method to determine the exact value of D_4^H(n,k,1) for n≤ 12 or k∈{1,2,3,n-1,n-2,n-3}, where D_4^H(n,k,1) denotes the largest minimum distance among all quaternary linear [n,k] codes with one-dimensional Hermitian hull. As a consequence, we solve a conjecture proposed by Mankean and Jitman on the largest minimum distance of a quaternary linear code with one-dimensional Hermitian hull. As an application, we construct some binary entanglement-assisted quantum error-correcting codes (EAQECCs) from quaternary linear codes with one-dimensional Hermitian hull. Some of these EAQECCs are optimal codes, and some of them are better than previously known ones.
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