We give a survey of results and applications relating to the theory of Gröbner bases of ideals and modules where the coefficient ring is a finite commutative ring. For applications, we specialize to the case of a finite chain ring. We discuss and compare the main algorithms that may be implemented to compute Gröbner and (in the case of a chain ring) Szekeres-like bases. We give an account of a number of decoding algorithms for alternant codes over commutative finite chain rings. © 2009 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Byrne, E., & Mora, T. (2009). Gröbner bases over commutative rings and applications to coding theory. In Gröbner Bases, Coding, and Cryptography (pp. 239–261). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-93806-4_14
Mendeley helps you to discover research relevant for your work.