Cryptology ePrint Archive: Report 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.

Category / Keywords: foundations / Linear code, minimal code, weight distribution, weakly regular plateaued function, unbalanced function

Date: received 19 Mar 2021, last revised 1 May 2021

Contact author: sinakahmet at gmail com

Available format(s): PDF | BibTeX Citation

Note: I have corrected the abstract and removed some parts of the manuscript.

Version: 20210502:013654 (All versions of this report)

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