The aim of this work is to algebraically describe the relative generalized Hamming weights of evaluation codes. We give a lower bound for these weights in terms of a footprint bound. We prove that this bound can be sharp. We compute the next-to-minimal weight of toric codes over hypersimplices of degree 1.

翻译：这项工作的目的是用代数来描述评估代码相对普遍的含重重量。我们用脚印为这些重量设定一个较低的界限。我们证明这一界限是锐利的。我们计算了比第1级轻度高的次到最低的对等编码的次至最低重量。