de Mathématiques de Luminy
The second weight of generalized Reed-Muller codes
The second weight of the Generalized Reed-Muller code of order d over the finite field with q elements is now known for d < q and d > (n − 1)(q − 1). In this paper, we determine the second weight for the other values of d which are not multiple of q − 1 plus 1. For d = a(q − 1) + 1 we only give an estimate.
Key words: finite field, footprint, generalized Reed-Muller code, Gröbner basis, Hamming weight, hypersurface, second weight, weight distribution