Date Available
5-22-2012
Year of Publication
2012
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dr. Heide Gluesing-Luerssen
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
