The generalized Goppa codes and related discrete designs from Hermitian surfaces in PG(3,s2)*
on Coding theory and applications
Weight polarization and divisibility
Discrete Mathematics - Coding Theory
Divisibility of codes meeting the Griesmer bound
Journal of Combinatorial Theory Series A
Designs, Codes and Cryptography
Codes defined by forms of degree 2 on Hermitian surfaces and Sørensen's conjecture
Finite Fields and Their Applications
Functional codes arising from quadric intersections with Hermitian varieties
Finite Fields and Their Applications
On the functional codes defined by quadrics and Hermitian varieties
Designs, Codes and Cryptography
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We study the functional codes of order h defined by G. Lachaud on a non-degenerate Hermitian variety, by exhibiting a result on divisibility for all the weights of such codes. In the case where the functional code is defined by evaluating quadratic functions on the non-degenerate Hermitian surface, we list the first five weights, describe the geometrical structure of the corresponding quadrics and give a positive answer to a conjecture formulated on this question by Edoukou (2009) [8]. The paper ends with two conjectures. The first is about the divisibility of the weights in the functional codes. The second is about the minimum distance and the distribution of the codewords of the first 2h+1 weights.