Linear Codes Obtained from Projective and Grassmann Bundles on Curves
Keyword(s):
Set Up
◽
We use split vector bundles on an arbitrary smooth curve defined over Fq to get linear codes (following the general set-up considered by S. H. Hansen and T. Nakashima), generalizing two quoted results by T. Nakashima. If p ≠ 2 for all integers d, g ≥ 2, r > 0 such that either r is odd or d is even we prove the existence of a smooth curve C of genus g defined over Fq and a p-semistable vector bundle E on C such that rank(E) = r, deg(E) = d and E is defined over Fq. Most results for particular curves are obtained taking double coverings or triple coverings of elliptic curves.
Keyword(s):
2020 ◽
Vol 117
(9)
◽
pp. 4546-4558
◽
Keyword(s):
Keyword(s):
2003 ◽
Vol 204
(2)
◽
pp. 355-398
◽
2011 ◽
Vol 84
(2)
◽
pp. 255-260
2012 ◽
Vol 10
(2)
◽
pp. 299-369
◽
Keyword(s):
Keyword(s):