We introduce a new concept “geometric extending” for linear codes over finite fields and consider the extendability of divisible codes. As an application, we construct new Griesmer ${[n,5,d]}_q$ codes for $3q^4-5q^3+1\le d\le 3q^4-5q^3+q^2$ with $q\ge 3$, combining the known geometric methods such as projective dual, geometric extending and geometric puncturing.

中文翻译：

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可分码的几何扩展和新线性码的构造

我们为有限域上的线性代码引入了新概念“几何扩展”，并考虑了可分代码的可扩展性。作为应用程序，我们构造了新的Griesmer${[ñ，5，d]}_q$ 的代码 $3q^4-5q^3+\mathrm{1个}\le d\le 3q^4-5q^3+q^2$ 与 $q\ge 3$，结合了已知的几何方法，例如射影对偶，几何扩展和几何穿刺。