The extended coset leader weight enumerator of a twisted cubic code
Combinatorics
2021-04-13 v2
Abstract
The extended coset leader weight enumerator of the generalized Reed-Solomon code is computed. The computation is considered as a question in finite geometry. For this we need the classification of the points, lines and planes in the projective three space under projectivities that leave the twisted cubic invariant. A line in three space determines a rational function of degree at most three and vice versa. Furthermore the double point scheme of a rational function is studied. The pencil of a true passant of the twisted cubic, not in an osculation plane gives a curve of genus one as double point scheme. With the Hasse-Weil bound on Fq-rational points we show that there is a 3-plane containing the passant.
Keywords
Cite
@article{arxiv.2103.16904,
title = {The extended coset leader weight enumerator of a twisted cubic code},
author = {Aart Blokhuis and Ruud Pellikaan and Tamás Szőnyi},
journal= {arXiv preprint arXiv:2103.16904},
year = {2021}
}