Subcodes of the Projective Generalized Reed-Muller Codes Spanned by Minimum-Weight Vectors

We use methods of Mortimer [19] to examine the subcodes spanned by minimumweight vectors of the projective generalized Reed-Muller codes and their duals. These methods provide a proof, alternative to a dimension argument, that neither the projective generalized Reed-Muller code of order r and of length qm -1 q-1 over the finite field Fq of prime-power order q, nor its dual, is spanned by its minimum-weight vectors for 0 < r < m - 1 unless q is prime. The methods of proof are the projective analogue of those developed in [17], and show that the codes spanned by the minimum-weight vectors are spanned over Fq by monomial functions in the m variables. We examine the same question for the subfield subcodes and their duals, and make a conjecture for the

• Type: Conference
• Year: 2002
• Where: DCC
• Authors: Peng Ding, Jennifer D. Key
• Keywords: Computer Graphics, DCC 2002, Finite Field Fq, Projective Analogue, Projective Generalized Reed-muller