TY - JOUR
T1 - Projective parameterized linear codes
AU - González Sarabia, Manuel
AU - Rentería Márquez, Carlos
AU - Sarmiento Rosales, Eliseo
N1 - Publisher Copyright:
© 2015, Ovidius University. All Rights Reserved.
PY - 2015
Y1 - 2015
N2 - In this paper we estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We find the length of these codes and we give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishing ideal of the projective torus. Also we find an upper bound for the minimum distance and, in some cases, we give some lower bounds for the regularity index and the minimum distance. These lower bounds work in several cases, particularly for any projective parameterized code associated to the incidence matrix of uniform clutters and then they work in the case of graphs.
AB - In this paper we estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We find the length of these codes and we give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishing ideal of the projective torus. Also we find an upper bound for the minimum distance and, in some cases, we give some lower bounds for the regularity index and the minimum distance. These lower bounds work in several cases, particularly for any projective parameterized code associated to the incidence matrix of uniform clutters and then they work in the case of graphs.
KW - Minimum distance
KW - Parameterized code
KW - Projective space
KW - Regularity index
UR - http://www.scopus.com/inward/record.url?scp=84928948176&partnerID=8YFLogxK
U2 - 10.1515/auom-2015-0039
DO - 10.1515/auom-2015-0039
M3 - Artículo
SN - 1224-1784
VL - 23
SP - 223
EP - 240
JO - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
JF - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
IS - 2
ER -