2 research outputs found
A class of linear codes with few weights
Linear codes have been an interesting topic in both theory and practice for
many years. In this paper, a class of -ary linear codes with few weights are
presented and their weight distributions are determined using Gauss periods.
Some of the linear codes obtained are optimal or almost optimal with respect to
the Griesmer bound. As s applications, these linear codes can be used to
construct secret sharing schemes with nice access structures
Optimal few-weight codes from simplicial complexes
Recently, some infinite families of binary minimal and optimal linear codes
are constructed from simplicial complexes by Hyun {\em et al}. Inspired by
their work, we present two new constructions of codes over the ring by employing simplicial complexes. When the simplicial complexes
are all generated by a maximal element, we determine the Lee weight
distributions of two classes of the codes over . Our
results show that the codes have few Lee weights. Via the Gray map, we obtain
an infinite family of binary codes meeting the Griesmer bound and a class of
binary distance optimal codes.Comment: 17 pages, To appear in IEEE I