Let m be a positive integer, and γ be a non-zero element of ${\mathbb{F}}_{2^m}$. The Lee distance of all cyclic codes and $(1+u\gamma )$-constacyclic codes of length $2^s$ over ${\mathbb{F}}_{2^m}+u{\mathbb{F}}_{2^m}$ is completely determined. In particular, it is shown that the Lee distance of such codes is independent of the choice of a trace orthogonal basis of ${\mathbb{F}}_{2^m}$.

中文翻译：

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F2m+uF2m 上长度为 2s 的循环和 (1 + uγ)-constacyclic 代码的 Lee 距离

令m为正整数，γ为非零元素${\mathbb{F}}_{2^{米}}$. 所有循环码的 Lee 距离和$(1+你\gamma )$- 长度的恒循环码 $2^{秒}$ 结束 ${\mathbb{F}}_{2^{米}}+你{\mathbb{F}}_{2^{米}}$是完全确定的。特别是，它表明这种代码的 Lee 距离独立于道正交基的选择${\mathbb{F}}_{2^{米}}$.