On the minimum distance, minimum weight codewords, and the dimension of projective Reed-Muller codes
Sudhir R. Ghorpade, Rati Ludhani · Advances in Mathematics of Communications · 2023
We give an alternative proof of the formula for the minimum distance of a projective Reed-Muller code of an arbitrary order. It leads to a complete characterization of the minimum weight codewords of a projective Reed-Muller code. This is then used to determine the number of minimum weight codewords of a projective Reed-Muller code. Various formulas for the dimension of a projective Reed-Muller code, and their equivalences are also discussed.