Date of Award
Doctor of Philosophy
Dr. Jay Wood
Dr. Annegret Paul
Dr. David Richter
Dr. Jens Zumbragel
MacWilliams extension theorem, MacWilliams identities
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.
Abdelghany, Noha, "On Codes Over Rings: The MacWilliams Extension Theorem and the MacWilliams Identities" (2020). Dissertations. 3591.