Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over \(\mathbb {F}_q\) having large minimum weights for \(q \in \{2,3\}\). Using the characterization, for arbitrary n, we determine the largest minimum weights among LCD [n, k] codes over \(\mathbb {F}_q\), where \((q,k) \in \{(2,4), (3,2),(3,3)\}\). Moreover, for arbitrary n, we give a complete classification of optimal LCD [n, k] codes over \(\mathbb {F}_q\), where \((q,k) \in \{(2,3), (2,4), (3,2),(3,3)\}\).

线性互补对偶（LCD）代码是与它们的对偶平凡相交的线性代码。我们给出了\（\ mathbb {F} _q \）上LCD代码的表征，该代码具有较大的\（q \ in \ {2,3 \} \）\权重。使用该特征，对于任意n，我们确定\ [\ mathbb {F} _q \）上LCD [ n，  k ]代码中最大的最小权重，其中\（（q，k）\ in \ {（2,4 ），（3,2），（3,3）\} \）。此外，对于任意n，我们给出\（\ mathbb {F} _q \）上最优LCD [ n，  k ]代码的完整分类，其中\（（q，k）\ in \ {（2,3），（2,4），（3,2），（3,3）\} \）中。