On cosets weight distributions of the doubly-extended Reed-Solomon codes of codimension 4
Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco · arXiv (Cornell University) · 2020
We consider the $[q+1,q-3,5]_q3$ generalized doubly-extended Reed-Solomon code of codimension $4$ as the code associated with the twisted cubic in the projective space $\mathrm{PG}(3,q)$. Basing on the point-plane incidence matrix of $\mathrm{PG}(3,q)$, we obtain the number of weight 3 vectors in all the cosets of the considered code. This allows us to classify the cosets by their weight distributions and to obtain these distributions. The weight of a coset is the smallest Hamming weight of any vector in the coset. For the cosets of equal weight having distinct weight distributions, we prove that the difference between the $w$-th components, $3