On near-MDS codes and caps

2021/06/07 by Ceria, Michela, Cossidente, Antonio, Marino, Giuseppe +1 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.03402

Abstract

Several classes of near-MDS codes of \rm 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 \cal W(3, q) or starting from the q+1 points of a twisted cubic of \rm PG(3, q). As a by-product two classes of complete caps of \rm PG(4,q) of size 2q²-q ± √(2q) + 2 are exhibited.

Cited by

• On the equivalence of NMDS codes

Related

• Near MDS codes from oval polynomials
• Tables, bounds and graphics of the smallest known sizes of complete caps in the spaces PG(3,q) and PG(4,q)
• On planes through points off the twisted cubic in PG(3,q) and multiple covering codes
• Extended codes and deep holes of MDS codes
• A note on short minimal codes from subgeometries