Skew Reed-Muller codes
Willi Geiselmann, Félix Ulmer · Contemporary mathematics - American Mathematical Society · 2019
We extend the classical Reed-Muller codes by using non-commutative iterated skew polynomial rings instead of classical commutative polynomial rings. This involves the construction of iterated skew polynomial rings and the definition of the notion of points and evaluation at those points for iterated skew polynomials. Our approach is based on the notion of a left module Gröbner basis in iterated skew polynomial rings.