====== Lucas Sabalka (Binghamton) ======

====== Projection-Forcing Multisets of Weight Changes ======

===== Abstract for the Combinatorics Seminar 2009 February 3 =====

Let F be a finite field. The //Hamming weight// of a vector is the number of nonzero entries. A multiset S of integers is called //projection forcing// if every linear map φ: F<sup>n</sup> —> F<sup>m</sup>, whose multiset of weight changes, {w(φ(v)−w(v)}, is S, is a coordinate projection up to permutation of entries. The MacWilliams Extension Theorem from coding theory says that S = {0, 0, ..., 0} is projection forcing.

In work with Josh Brown Kramer, we give a (super-polynomial) algorithm to determine whether or not a given set S is projection forcing. we also give a condition that can be checked in polynomial time that implies that S is projection forcing.


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