You are looking at a specific version 20210322:193238 of this paper. See the latest version.

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)
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
Creative Commons Attribution
CC BY
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.