10 research outputs found
A new class of three-weight linear codes from weakly regular plateaued functions
Linear codes with few weights have many applications in secret sharing
schemes, authentication codes, communication and strongly regular graphs. In
this paper, we consider linear codes with three weights in arbitrary
characteristic. To do this, we generalize the recent contribution of Mesnager
given in [Cryptography and Communications 9(1), 71-84, 2017]. We first present
a new class of binary linear codes with three weights from plateaued Boolean
functions and their weight distributions. We next introduce the notion of
(weakly) regular plateaued functions in odd characteristic and give
concrete examples of these functions. Moreover, we construct a new class of
three-weight linear -ary codes from weakly regular plateaued functions and
determine their weight distributions. We finally analyse the constructed linear
codes for secret sharing schemes.Comment: The Extended Abstract of this work was submitted to WCC-2017 (the
Tenth International Workshop on Coding and Cryptography
Minimal linear codes from characteristic functions
Minimal linear codes have interesting applications in secret sharing schemes
and secure two-party computation. This paper uses characteristic functions of
some subsets of to construct minimal linear codes. By properties
of characteristic functions, we can obtain more minimal binary linear codes
from known minimal binary linear codes, which generalizes results of Ding et
al. [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018]. By
characteristic functions corresponding to some subspaces of , we
obtain many minimal linear codes, which generalizes results of [IEEE Trans.
Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018] and [IEEE Trans. Inf.
Theory, vol. 65, no. 11, pp. 7067-7078, 2019]. Finally, we use characteristic
functions to present a characterization of minimal linear codes from the
defining set method and present a class of minimal linear codes