Projection-forcing multisets of weight changes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:117

Article

Kramer, Josh Brown¹  Sabalka, Lucas² 

[1] Illinois Wesleyan Univ, Bloomington, IL 61701 USA

[2] SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA

关键词: MacWilliams Extension Theorem;    Projections;    Finite fields;    Coding theory;   

DOI  :  10.1016/j.jcta.2010.01.005

来源: Elsevier

【 摘 要 】

Let F be a finite field. A multiset S of integers is projection-forcing if for every linear function phi : F(n) -> 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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free