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Abstract We introduce quaternary modified four μ -circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four μ -circulant Hermitian self-dual codes. We also construct quaternary modified four μ -circulant Hermitian self-dual codes having large minimum weights. Two quaternary Hermitian self-dual 56, 28, 16 codes are constructed for the first time. These codes improve the previously known lower bound on the largest minimum weight among all quaternary (linear) 56, 28 codes. In addition, these codes imply the existence of a quantum [56, 0, 16] code.
Masaaki Harada (Tue,) studied this question.