Projection-Forcing Multisets of Weight Changes

Details Projection-Forcing Multisets of Weight Changes Projection-Forcing Multisets of Weight Changes

2009-03-25

arxiv.org/abs/0903.4237v2

Journal of Combinatorial Theory, Series A, 117(8): 1136-1142, 2010

Mathematics

Combinatorics

11 Pages

Scientific paper

10.1016/j.jcta.2010.01.005

Let $F$ be a finite field. A multiset $S$ of integers is projection-forcing if for every linear function $\phi : F^n \to F^m$ whose multiset of weight changes is $S$, $\phi$ 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.

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