We show that any ternary Euclidean (resp. quaternary Hermitian) linear complementary dual $[n,k]$ code contains a Euclidean (resp. Hermitian) linear complementary dual $[n,k-1]$ subcode for $2\le k\le n$. As a consequence, we derive a bound on the largest minimum weights among ternary Euclidean linear complementary dual codes and quaternary Hermitian linear complementary dual codes.

中文翻译：

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线性互补双码子码说明

我们表明，任何三元欧几里得（分别为四元厄米）线性互补对偶 $[ñ，ķ]$ 代码包含欧几里得（分别为厄米）和线性互补对偶 $[ñ，ķ-\mathrm{1个}]$ 的子代码 $2\le ķ\le ñ$。结果，我们推导了三元欧几里德线性互补双码和四元厄米线性互补双码中最大最小权重的界。