I begin a PhD in coding theory next fall, and it concerns coding over certain types of rings (e.g. finite chain rings) instead of fields, and in consequence submodule codes. I have a fair amount of knowledge in comm. algebra and have had a standard undergraduate coding theory over finite fields course, so I was wondering:
Is there a well-respected graduate text, or a good set of notes, covering more advanced tools in algebraic coding theory?
Thanks, and let me know if I need to clarify anything.
The following relatively recent book is the only one I know about. Its contents include:
Quasicyclic codes over chain rings
MDR codes
Convolutional Codes over Rings
Shi, Alahmadi and Sole, Codes and Rings: Theory and Practice, Academic Press, 2017