Classification of optimal quaternary Hermitian LCD codes of dimension $2$

Abstract

Hermitian linear complementary dual codes are linear codes whose intersections with their Hermitian dual codes are trivial. The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for each length. We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension $2$. Hermitian linear complementary dual codes are linear codes whose intersections with their Hermitian dual codes are trivial. The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for each length. We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension $2$.