TY - JOUR
T1 - On the dual minimum distance and minimum weight of codes from a quotient of the Hermitian curve
AU - Ballico, Edoardo
AU - Ravagnani, Alberto
PY - 2013/11
Y1 - 2013/11
N2 - In this paper we study evaluation codes arising from plane quotients of the Hermitian curve, defined by affine equations of the form y q + y = x m, q being a prime power and m a positive integer which divides q + 1. The dual minimum distance and minimum weight of such codes are studied from a geometric point of view. In many cases we completely describe the minimum-weight codewords of their dual codes through a geometric characterization of the supports, and provide their number. Finally, we apply our results to describe Goppa codes of classical interest on such curves.
AB - In this paper we study evaluation codes arising from plane quotients of the Hermitian curve, defined by affine equations of the form y q + y = x m, q being a prime power and m a positive integer which divides q + 1. The dual minimum distance and minimum weight of such codes are studied from a geometric point of view. In many cases we completely describe the minimum-weight codewords of their dual codes through a geometric characterization of the supports, and provide their number. Finally, we apply our results to describe Goppa codes of classical interest on such curves.
KW - Evaluation code
KW - Goppa code
KW - Minimum distance
KW - Minimum-weight codeword
KW - Quotient of Hermitian curve
UR - http://www.scopus.com/inward/record.url?scp=84887474090&partnerID=8YFLogxK
U2 - 10.1007/s00200-013-0206-z
DO - 10.1007/s00200-013-0206-z
M3 - Article
AN - SCOPUS:84887474090
SN - 0938-1279
VL - 24
SP - 343
EP - 354
JO - Applicable Algebra in Engineering, Communication and Computing
JF - Applicable Algebra in Engineering, Communication and Computing
IS - 5
ER -