**Problem of the Week**

**BUGCAT**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

**BingAWM**

**Math Club**

You are here: Homepage » Seminars - Academic year 2023-24 » Combinatorics Seminar » Lucas Sabalka (Binghamton)

seminars:comb:abstract.200902sab

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^{n} —> F^{m}, 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.

seminars/comb/abstract.200902sab.txt · Last modified: 2020/01/29 14:03 (external edit)

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 3.0 Unported