A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes. (English) Zbl 07926035
Summary: We introduce quaternary modified four \(\mu\)-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four \(\mu\)-circulant Hermitian self-dual codes. We also construct quaternary modified four \(\mu\)-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.
MSC:
| 94B05 | Linear codes (general theory) |
References:
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