Solving the key equation of alternant codes with Groebner basis.
Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3786
dept.math [at] unitn.it
Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
- Relatore: Matteo Bonini (Dottorando Dip.to Matematica Università di Trento)
Abstract: Alternant codes are a large and powerful family of error correcting codes including BCH, RS and 1-variable Goppa codes.
In this seminar we concentrate on the solution of the key equation for their decoding using Fitzpatrick's method, which is based on Groebner basis techniques. In decoding these codes a particular solution is sought as a couple of polynomials being relatively prime and satisfying certain degree conditions.
In particular these requirements specify uniquely as the minimal element of the module of the solutions with respect to a certain term order and that may be determined from an appropriate Grobner basis.
Referente: Massimiliano Sala