On algebraic structure of the Reed-Muller codes

Keywords: Reed-Muller codes, finite field, interpolation polynomial, Jennings basis

Abstract

It is known that the Reed-Muller codes over a prime field may be described as the radical powers of a modular group algebra. In this paper, we give a new proof of the same result in a quotient of a polynomial ring. Special elements in a prime field are studied. An interpolation polynomial is introduced in order to characterize the coefficients of the Jennings polynomials.

Published
2021-09-16
Section
Articles