Quaternary Hermitian linear complementary dual codes

Makoto Araya; Masaaki Harada; Ken Saito

doi:10.1109/tit.2019.2949040

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arXiv · 1904.07517

Quaternary Hermitian linear complementary dual codes

Makoto Araya·Masaaki Harada·Ken Saito

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Abstract

The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension $2$. In this paper, we give some conditions for the nonexistence of quaternary Hermitian linear complementary dual codes with large minimum weights. As an application, we completely determine the largest minimum weights for dimension $3$, by using a classification of some quaternary codes. In addition, for a positive integer $s$, a maximal entanglement entanglement-assisted quantum $[[21s+5,3,16s+3;21s+2]]$ codes is constructed for the first time from a quaternary Hermitian linear complementary dual $[26,3,19]$ code.

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Makoto Araya, Masaaki Harada, Ken Saito. 2019-04-16. Quaternary Hermitian linear complementary dual codes. https://doi.org/10.1109/tit.2019.2949040

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