Paper 2021/371
Construction of minimal linear codes with few weights from weakly regular plateaued functions
Ahmet Sinak
Abstract
The construction of linear (minimal) codes from functions over finite fields has been greatly studied in the literature since determining the parameters of linear codes based on functions is rather easy due to the nice structures of functions. In this paper, we derive 3-weight and 4-weight linear codes from weakly regular plateaued unbalanced functions in the recent construction method of linear codes over the odd characteristic finite fields. The Hamming weights and their weight distributions for proposed codes are determined by using the Walsh transform values and Walsh distribution of the employed functions, respectively. We next derive projective 3-weight punctured codes with good parameters from the constructed codes. These punctured codes may be almost optimal due to the Griesmer bound, and they can be employed to design association schemes. We lastly show that all constructed codes are minimal, which approves that they can be employed to design high democratic secret sharing schemes.
Note: I have corrected the abstract and removed some parts of the manuscript.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Linear codeminimal codeweight distributionweakly regular plateaued functionunbalanced function
- Contact author(s)
- sinakahmet @ gmail com
- History
- 2021-05-02: revised
- 2021-03-22: received
- See all versions
- Short URL
- https://ia.cr/2021/371
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/371,
author = {Ahmet Sinak},
title = {Construction of minimal linear codes with few weights from weakly regular plateaued functions},
howpublished = {Cryptology ePrint Archive, Paper 2021/371},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/371}},
url = {https://eprint.iacr.org/2021/371}
}
