TY - JOUR
T1 - On the generalized Hamming weights of certain Reed-Muller-type codes
AU - González-Sarabia, Manuel
AU - Jaramillo, Delio
AU - Villarreal, Rafael H.
N1 - Publisher Copyright:
© 2020 Manuel González-Sarabia et al., published by Sciendo.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - There is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a family of a ne cartesian codes. If X is a set of projective points over a finite field we determine the basic parameters and the generalized Hamming weights of the Veronese type codes on X and their dual codes in terms of the basic parameters and the generalized Hamming weights of the corresponding projective Reed-Muller-type codes on X and their dual codes.
AB - There is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a family of a ne cartesian codes. If X is a set of projective points over a finite field we determine the basic parameters and the generalized Hamming weights of the Veronese type codes on X and their dual codes in terms of the basic parameters and the generalized Hamming weights of the corresponding projective Reed-Muller-type codes on X and their dual codes.
KW - Reed-Muller-type codes
KW - Veronese code
KW - generalized Hamming weights
KW - linear code
UR - http://www.scopus.com/inward/record.url?scp=85083891567&partnerID=8YFLogxK
U2 - 10.2478/auom-2020-0014
DO - 10.2478/auom-2020-0014
M3 - Artículo
AN - SCOPUS:85083891567
SN - 1224-1784
VL - 28
SP - 205
EP - 217
JO - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
JF - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
IS - 1
ER -