TY - JOUR
T1 - The second generalized Hamming weight of some evaluation codes arising from a projective torus
AU - González Sarabia, Manuel
AU - Camps, Eduardo
AU - Sarmiento, Eliseo
AU - Villarreal, Rafael H.
N1 - Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/7
Y1 - 2018/7
N2 - In this paper we give a formula for the second generalized Hamming weight of certain evaluation codes arising from a projective torus. This allows us to compute the corresponding weights of the codes parameterized by the edges of a complete bipartite graph. We determine some of the generalized Hamming weights of non-degenerate evaluation codes arising from a complete intersection in terms of the minimum distance, the degree and the a-invariant. It is shown that the generalized Hamming weights and the minimum distance have some similar behavior for parameterized codes These results are used to find the complete weight hierarchy of some codes.
AB - In this paper we give a formula for the second generalized Hamming weight of certain evaluation codes arising from a projective torus. This allows us to compute the corresponding weights of the codes parameterized by the edges of a complete bipartite graph. We determine some of the generalized Hamming weights of non-degenerate evaluation codes arising from a complete intersection in terms of the minimum distance, the degree and the a-invariant. It is shown that the generalized Hamming weights and the minimum distance have some similar behavior for parameterized codes These results are used to find the complete weight hierarchy of some codes.
KW - Complete intersection
KW - Evaluation code
KW - Generalized Hamming weight
KW - Parameterized code
UR - http://www.scopus.com/inward/record.url?scp=85047253011&partnerID=8YFLogxK
U2 - 10.1016/j.ffa.2018.05.002
DO - 10.1016/j.ffa.2018.05.002
M3 - Artículo
SN - 1071-5797
VL - 52
SP - 370
EP - 394
JO - Finite Fields and their Applications
JF - Finite Fields and their Applications
ER -