Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Jay Wood

Second Advisor

Dr. Annegret Paul

Third Advisor

Dr. David Richter

Fourth Advisor

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.

Access Setting

Dissertation-Open Access

Included in

Mathematics Commons