On a beautiful foundational result in ring-linear coding theory

Vortrag von Dr. Marcus Greferath

Sprecher eingeladen von: Prof. Dr. Joachim Rosenthal

Datum: 31.05.17  Zeit: 15.00 - 16.00  Raum: Y27H28

One of the most important foundational results in Algebraic ring-linear Coding Theory states that Hamming isometries between ring-linear codes are restrictions of monomial automorphisms of the ambient space, where we add, that this result is true for any finite ring, as long we utilize its character module as alphabet of the according coding theory.
Newer investigations have dealt with the question, if there are further isometries (preserving different weight functions) that allow for monomial representations of this type. This is, what this talk will address, and we will present a sufficiently general result, that speaks for itself already because of its inherent mathematical beauty.