Title: On Skew-Constacyclic Codes

Abstract: Cyclic codes are a well-known class of linear block codes with efficient decoding algorithms. In recent years they have been generalized to skew-constacyclic codes; such a generalization has previously been shown to be useful. After a brief introduction of skew-polynomial rings and their quotient modules, which we use to study skew-constacyclic codes algebraically, we motivate and define a notion of idempotent elements in these quotient modules. We are particularly concerned with the existence and uniqueness of idempotents that generate a given submodule; as such, we generalize relevant results from previous work on skew-constacyclic codes by Gao/Shen/Fu in 2013 and well-known results from the classical case.