Projection-forcing multisets of weight changes |
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Authors: | Josh Brown Kramer |
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Institution: | a Illinois Wesleyan University, Mathematics and Computer Science, 1312 Park Street, Bloomington, IL, United States b Department of Mathematical Sciences, Binghamton University, SUNY, Binghamton, NY 13902-6000, United States |
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Abstract: | Let F be a finite field. A multiset S of integers is projection-forcing if for every linear function ?:Fn→Fm whose multiset of weight changes is S, ? 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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Keywords: | MacWilliams Extension Theorem Projections Finite fields Coding theory |
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