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Date Available
5-22-2012
Year of Publication
2012
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Mathematics
Faculty
Dr. Heide Gluesing-Luerssen
Faculty
Dr. Peter A. Perry
Abstract
In this thesis we revisit some classical results about the MacWilliams equivalence theorems for codes over fields and rings. These theorems deal with the question whether, for a given weight function, weight-preserving isomorphisms between codes can be described explicitly. We will show that a condition, which was already known to be sufficient for the MacWilliams equivalence theorem, is also necessary. Furthermore we will study a local-global property that naturally generalizes the MacWilliams equivalence theorems. Making use of F-partitions, we will prove that for various subgroups of the group of invertible matrices the local-global extension principle is valid.
Recommended Citation
Barra, Aleams, "Equivalence Theorems and the Local-Global Property" (2012). Theses and Dissertations--Mathematics. 5.
https://uknowledge.uky.edu/math_etds/5
