投影-强制权值变化的多集
Projection-Forcing Multisets of Weight Changes
摘要：
设$F$是一个有限域。整数的多集$S$是投影强迫的，如果对于每个权值变化的多集是$S$的线性函数$ϕ: F^n \to F^m$，$ϕ$是直到项的置换和缩放的坐标投影。来自编码理论的麦克威廉姆斯扩展定理说，$S = \{0, 0, ..., 0\}$是投影强迫。我们给出了一个（超多项式）算法来确定是否一个给定的$S$是投影强迫。我们还给出了一个条件，可以在多项式时间内检查，这意味着$S$是投影强迫。这个结果是MacWilliams扩张定理和第一作者工作的推广。
英文摘要：
Let $F$ be a finite field. A multiset $S$ of integers is projection-forcing if for every linear function $ϕ: F^n \to F^m$ whose multiset of weight changes is $S$, $ϕ$ is a coordinate projection up to permutation and scaling of entries. The MacWilliams Extension Theorem from coding theory says that $S = \{0, 0, ..., 0\}$ is projection-forcing. We give a (super-polynomial) algorithm to determine whether or not a given $S$ is projection-forcing. We also give a condition that can be checked in polynomial time that implies that $S$ is projection-forcing. This result is a generalization of the MacWilliams Extension Theorem and work by the first author.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
