2024/05/20 by Krishna Kaipa, Kaipa, Krishna, Puspendu Pradhan +1
Computer Science · #Coding theory and cryptography
paper · pdf · doi:10.48550/arxiv.2405.12011
The problem studied in this work is to determine the higher weight spectra of the Projective Reed-Muller codes associated to the Veronese 3-fold \mathcal V in PG(9,q), which is the image of the quadratic Veronese embedding of PG(3,q) in PG(9,q). We reduce the problem to the following combinatorial problem in finite geometry: For each subset S of \mathcal V, determine the dimension of the linear subspace of PG(9,q) generated by S. We develop a systematic method to solve the latter problem. We implement the method for q=3, and use it to obtain the higher weight spectra of the associated code. The case of a general finite field \mathbb Fq will be treated in a future work.