3 papers
cs.IT2023
A Gröbner Approach to Dual-Containing Cyclic Left Module -Codes over Finite Commutative Frobenius Rings
Hedongliang Liu, Cornelia Ott, Felix Ulmer
For a skew polynomial ring where is a commutative Frobenius ring, an endomorphism of and a -derivation of , we consider cyclic left module codes…
cs.IT2015
Duality Preserving Gray Maps for Codes over Rings
Steve Szabo, Felix Ulmer
Given a finite ring which is a free left module over a subring of , two types of -bases, pseudo-self-dual bases (similar to trace orthogonal bases) and symmetric base…
math.RA2006
Skew-cyclic codes
Delphine Boucher, Willi Geiselmann, Félix Ulmer
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the ob…