On algebraic structure of the Reed-Muller codes
DOI:
https://doi.org/10.26493/2590-9770.1417.02aKeywords:
Reed-Muller codes, finite field, interpolation polynomial, Jennings basisAbstract
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.