824 research outputs found
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
Linear Codes from Some 2-Designs
A classical method of constructing a linear code over \gf(q) with a
-design is to use the incidence matrix of the -design as a generator
matrix over \gf(q) of the code. This approach has been extensively
investigated in the literature. In this paper, a different method of
constructing linear codes using specific classes of -designs is studied, and
linear codes with a few weights are obtained from almost difference sets,
difference sets, and a type of -designs associated to semibent functions.
Two families of the codes obtained in this paper are optimal. The linear codes
presented in this paper have applications in secret sharing and authentication
schemes, in addition to their applications in consumer electronics,
communication and data storage systems. A coding-theory approach to the
characterisation of highly nonlinear Boolean functions is presented
On the Weight Distribution of Codes over Finite Rings
Let R > S be finite Frobenius rings for which there exists a trace map T from
R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is
an S-linear subring-subcode of a left linear code over R. We consider functions
f for which the homogeneous weight distribution of C can be computed. In
particular, we give constructions of codes over integer modular rings and
commutative local Frobenius that have small spectra.Comment: 18 p
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