8 research outputs found
The Subfield Codes of Some Few-Weight Linear Codes
Subfield codes of linear codes over finite fields have recently received a
lot of attention, as some of these codes are optimal and have applications in
secrete sharing, authentication codes and association schemes. In this paper,
the -ary subfield codes of six different families of
linear codes are presented, respectively. The parameters and
weight distribution of the subfield codes and their punctured codes
are explicitly determined. The parameters of the duals of
these codes are also studied. Some of the resultant -ary codes
and their dual codes are optimal
and some have the best known parameters. The parameters and weight enumerators
of the first two families of linear codes are also settled,
among which the first family is an optimal two-weight linear code meeting the
Griesmer bound, and the dual codes of these two families are almost MDS codes.
As a byproduct of this paper, a family of quaternary
Hermitian self-dual code are obtained with . As an application,
several infinite families of 2-designs and 3-designs are also constructed with
three families of linear codes of this paper.Comment: arXiv admin note: text overlap with arXiv:1804.06003,
arXiv:2207.07262 by other author