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


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Article Info

DATE

2019-03

AUTHORS

Sihem Mesnager, Ferruh Özbudak, Ahmet Sınak

ABSTRACT

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. More... »

PAGES

463-480

References to SciGraph publications

  • 2014. Characterizations of Plateaued and Bent Functions in Characteristic $$p$$ in SEQUENCES AND THEIR APPLICATIONS - SETA 2014
  • 2017-01. Linear codes with few weights from weakly regular bent functions based on a generic construction in CRYPTOGRAPHY AND COMMUNICATIONS
  • 2016-11. Linear codes with two or three weights from quadratic Bent functions in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2013-01. A construction of bent functions from plateaued functions in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1999. Plateaued Functions in INFORMATION AND COMMUNICATION SECURITY
  • 2016. Results on Characterizations of Plateaued Functions in Arbitrary Characteristic in CRYPTOGRAPHY AND INFORMATION SECURITY IN THE BALKANS
  • 2003. Covering and Secret Sharing with Linear Codes in DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
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    http://scigraph.springernature.com/pub.10.1007/s10623-018-0556-4

    DOI

    http://dx.doi.org/10.1007/s10623-018-0556-4

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