15 research outputs found
The weight distributions of a class of cyclic codes III
Recently, the weight distributions of the duals of the cyclic codes with two
zeros have been obtained for several cases. In this paper we solve one more
special case. The problem of finding the weight distribution is transformed
into a problem of evaluating certain character sums over finite fields, which
in turn can be solved by using the Jacobi sums directly
Five Families of Three-Weight Ternary Cyclic Codes and Their Duals
As a subclass of linear codes, cyclic codes have applications in consumer
electronics, data storage systems, and communication systems as they have
efficient encoding and decoding algorithms. In this paper, five families of
three-weight ternary cyclic codes whose duals have two zeros are presented. The
weight distributions of the five families of cyclic codes are settled. The
duals of two families of the cyclic codes are optimal
Weight distributions of cyclic codes with respect to pairwise coprime order elements
Let be an extension of a finite field with . Let
each be of order in and for .
We define a cyclic code over by
where
and . In this paper,
we present a method to compute the weights of . Further, we determine the weight distributions of the cyclic codes
and .Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:1306.527
Weight distribution of two classes of cyclic codes with respect to two distinct order elements
Cyclic codes are an interesting type of linear codes and have wide
applications in communication and storage systems due to their efficient
encoding and decoding algorithms. Cyclic codes have been studied for many
years, but their weight distribution are known only for a few cases. In this
paper, let be an extension of a finite field and ,
we determine the weight distribution of the cyclic codes c(a, b)=(\mbox {Tr}_{r/q}(ag_1^0+bg_2^0), \ldots, \mbox
{Tr}_{r/q}(ag_1^{n-1}+bg_2^{n-1})), g_1, g_2\in \Bbb F_r, in the following
two cases: (1) \ord(g_1)=n, n|r-1 and ; (2) \ord(g_1)=n,
, \ord(g_2)=\frac n 2, and