A new class of three-weight linear codes from weakly regular plateaued functions
Abstract
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.
Keywords
Cite
@article{arxiv.1703.08362,
title = {A new class of three-weight linear codes from weakly regular plateaued functions},
author = {Sihem Mesnager and Ferruh Özbudak and Ahmet Sınak},
journal= {arXiv preprint arXiv:1703.08362},
year = {2017}
}
Comments
The Extended Abstract of this work was submitted to WCC-2017 (the Tenth International Workshop on Coding and Cryptography)