Simplex and MacDonald Codes Over Finite Chain Rings and Their Gray Map Images

Vortrag von Sergi Sánchez Aragón

Sprecher eingeladen von: Prof. Dr. Joachim Rosenthal

Datum: 29.04.26  Zeit: 16.30 - 17.30  Raum: Y27H28

A linear code of length \(n\) over a finite chain ring \(R\) with residue field \(\mathbb{F}_q\) is a \(R\)-submodule of \(R^n\). A \(R\)-linear code is a code over \(\mathbb{F}_q\) (not necessarily linear) which is the generalized Gray map image of a linear code over \(R\).

In this talk, we present some of the basic properties of linear codes over finite chain rings, as well as the tools used to study linearity of \(R\)-linear codes.

Finally, we introduce the construction of linear simplex and MacDonald codes of type \(\alpha\) and \(\beta\) over a finite chain ring, showing their properties and those of their Gray map images.