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 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.

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

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

Contact author: sinakahmet at gmail com

Available format(s): PDF | BibTeX Citation

Note: I have corrected the title and author name.

Version: 20210322:193238 (All versions of this report)

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