Commutative Algebra and Coding Theory
Date:
A presentation (🇬🇧) for the final exam of the course Advanced Commutative Algebra . These slides where inspired by the wonderful book Codes, Cryptology and Curves with Computer Algebra containing two interesting intersections between coding theory and commutative algebra, that I have expanded and inserted in the slides (it is possible to have also the annotated version). The two main arguments are:
- A general method for decoding Cyclic codes using Groebner basis, called Cooper’s Philosophy. I have also proposed a working example of the decoding in MAGMA (here the code), where is possible also to change the parameters to obtain different examples.
- A link between Matroid and Coding theory, with some easy results.