The second weight of generalized Reed-Muller codes in most cases
The second weight of the Generalized Reed-Muller code of length q n and order d over the finite field with q elements is now known for d? ?(n???1)(q???1). In this paper, we determine the second weight for the other values of d which are not multiples of q???1 plus 1. For the special case d?=?a(q???1)?+?1 we give an estimate.
second weight generalized reed-muller code finite field footprint grbner basis hamming weight hypersurface weight distribution 11g25 11t71