Year of Publication
Doctor of Philosophy (PhD)
Arts and Sciences
Dr. Heide Gluesing-Luerssen
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.
Barra, Aleams, "Equivalence Theorems and the Local-Global Property" (2012). Theses and Dissertations--Mathematics. 5.