Linear codes from weakly regular plateaued functions and their secret sharing schemes

Date

2019-03-01

Author

Mesnager, Sihem
Özbudak, Ferruh
Sinak, Ahmet

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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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Citation Formats

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.