A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes

Author:

Masaaki Harada

Keyword:

Computer Science, Information Theory, Information Theory (cs.IT), Combinatorics (math.CO)

journal:

date:

2024-01-27 00:00:00

Abstract

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.

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