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Linear codes from weakly regular plateaued functions and their secret sharing schemes
Date
2019-03-01
Author
Mesnager, Sihem
Özbudak, Ferruh
Sinak, Ahmet
Metadata
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Linear codes, the most significant class of codes in coding theory, have diverse applications in secret sharing schemes, authentication codes, communication, data storage devices and consumer electronics. The main objectives of this paper are twofold: to construct three-weight linear codes from plateaued functions over finite fields, and to analyze the constructed linear codes for secret sharing schemes. To do this, we generalize the recent contribution of Mesnager given in (Cryptogr Commun 9(1):71-84, 2017). We first introduce the notion of (non)-weakly regular plateaued functions over Fp, with p being an odd prime. We next construct three-weight linear p-ary (resp. binary) codes from weakly regular p-ary plateaued (resp. Boolean plateaued) functions and determine their weight distributions. We finally observe that the constructed linear codes are minimal for almost all cases, which implies that they can be directly used to construct secret sharing schemes with nice access structures. To the best of our knowledge, the construction of linear codes from plateaued functions over Fp, with p being an odd prime, is studied in this paper for the first time in the literature.
Subject Keywords
Binary linear codes
,
Linear p-ary codes
,
Secret sharing schemes
,
Weakly regular plateaued functions
,
Weight distribution
URI
https://hdl.handle.net/11511/35115
Journal
DESIGNS CODES AND CRYPTOGRAPHY
DOI
https://doi.org/10.1007/s10623-018-0556-4
Collections
Department of Mathematics, Article
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S. Mesnager, F. Özbudak, and A. Sinak, “Linear codes from weakly regular plateaued functions and their secret sharing schemes,”
DESIGNS CODES AND CRYPTOGRAPHY
, pp. 463–480, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35115.