AI 中文总结
该研究获得评估码广义汉明重量的足迹界与对偶足迹界的魏型对偶性，此对偶性也适用于其他界，同时证明了足迹界和对偶足迹界不能保证评估码族的渐近优良性。
AI 中文摘要
我们得到了评估码广义汉明重量的足迹界与对偶足迹界之间的魏型对偶性。这种对偶性也适用于安徒生 - 盖尔界和冯 - 饶界。我们还证明了足迹界和对偶足迹界不能用于保证一族评估码的渐近优良性。
英文摘要
We obtain a Wei-type duality between the footprint bound and the dual footprint bound for the generalized Hamming weights of an evaluation code. This duality applies between the Andersen-Geil and Feng-Rao bounds as well. We also prove that the footprint and dual footprint bounds cannot be used to guarantee the asymptotic goodness of a family of evaluation codes.
