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 $2$.
Highlights
Let F4 := {0, 1, ω, ω2} be the finite field of order four, where ω satisfies ω2 +ω +1 = 0
We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension 2
A quaternary [n, k, d] code is a linear subspace of Fn4 with dimension k and minimum weight d
Summary
It is known that C C if and only if G can be obtained from G by an elementary row operation, a permutation of the columns and multiplication of any column by a nonzero scalar It was shown in [6] that the upper bound of the minimum weight of the Hermitian LCD [n, 2, d] codes is given as follows: d≤. A method to classify optimal Hermitian LCD codes of dimension 2 is given. The complete classification of optimal Hermitian LCD codes of dimension 2 is given. It is shown that all inequivalent codes have distinct weight enumerators, which is used for the classification
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