On the second weight of generalized Reed-Muller codes

: Not much is known about the weight distribution of the generalized Reed-Muller code RMq(s, m) when q > 2, s > 2 and m 2 . Even the second weight is only known for values of s being smaller than or equal to q/2. In this paper we establish the second weight for values of s being smaller than q. For s greater than (m - 1)(q - 1) we then find the first s + 1 - (m - 1)(q - 1) weights. For the case m = 2 the second weight is now known for all values of s. The results are derived mainly by using Gr?bner basis theoretical methods.

• Type: Conference
• Year: 2008
• Where: DCC
• Authors: Olav Geil
• Keywords: Basis Theoretical Methods, Computer Graphics, DCC 2008