Date of Award
6-2020
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Dr. Jay Wood
Second Advisor
Dr. Annegret Paul
Third Advisor
Dr. David Richter
Fourth Advisor
Dr. Jens Zumbragel
Keywords
MacWilliams extension theorem, MacWilliams identities
Abstract
The MacWilliams extension theorem for code equivalence and the MacWilliams identities for weight enumerators of a code and its dual code are two of the most important results in classical coding theory. In this thesis, we study how much these two results could be extended to codes over more general alphabets, beyond finite fields. In particular, we study the MacWilliams extension theorem and the MacWilliams identities for codes over rings and modules equipped with general weight functions.
Access Setting
Dissertation-Open Access
Recommended Citation
Abdelghany, Noha, "On Codes Over Rings: The MacWilliams Extension Theorem and the MacWilliams Identities" (2020). Dissertations. 3591.
https://scholarworks.wmich.edu/dissertations/3591