Several classes of near-MDS codes of PG(3,q) are described. They are obtained either by considering the intersection of an elliptic quadric ovoid and a Suzuki-Tits ovoid of a symplectic polar space W(3,q) or starting from the q+1 points of a twisted cubic of PG(3,q). As a by-product two classes of complete caps of PG(4,q) of size 2q2−q±2q+2 are exhibited.
@article{arxiv.2106.03402,
title = {On near-MDS codes and caps},
author = {Michela Ceria and Antonio Cossidente and Giuseppe Marino and Francesco Pavese},
journal= {arXiv preprint arXiv:2106.03402},
year = {2021}
}