Skew-cyclic codes
Delphine Boucher, Willi Geiselmann, Félix Ulmer
Abstract
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 obtained codes share most properties of cyclic codes. Since there are much more skew-cyclic codes, this new class of codes allows to systematically search for codes with good properties. We give many examples of codes which improve the previously best known linear codes.
Create a lesson
Related papers
Hochschild cohomology of Temperley--Lieb algebras: a Kauffman diagram perspective
Viktor Lopatkin
Binomial Artin-Schelter Regular Algebras and Twisted Monoid Algebras
Vishal Bhatoy
Rings in which every semiprime left ideal is an intersection of prime left ideals
Jakob Cimprič
The finite basis problem for varieties modulo x3=0
Elena Kireeva, Alexei Krasilnikov, Vladimir Shchigolev
Extensions at Nonzero p-Characters for Cartan-Type Lie Algebras
Chao Ma
Counterexamples to a Cubic Nondegeneracy Conjecture
Santiago Pineda Montoya