Paper 2021/371
Construction of minimal linear codes with few weights from weakly regular plateaued functions
Ahmet Sinak
Abstract
The construction of linear codes from functions over finite fields has been extensively studied in the literature since determining the parameters of linear codes based on functions is rather easy due to the nice structure 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 finite fields of odd characteristics. 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 obtain association schemes. We also derive projective 2-weight and 3-weight subcodes with flexible dimensions from partially bent functions, and these subcodes can be employed to design strongly regular graphs. We finally show that all constructed codes are minimal, which approve that they can be employed to design high democratic secret sharing schemes.
Note: I have corrected the title and author name.
Metadata
- Available format(s)
- 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