Two or Three Weight Linear Codes from Non-Weakly Regular Bent Functions

Date

2022-05-01

Author

Özbudak, Ferruh
Pelen, Rumi Melih

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© 1963-2012 IEEE.Linear codes with few weights have applications in consumer electronics, communications, data storage systems, secret sharing, authentication codes, and association schemes. As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure computation of data between two parties. The construction of minimal linear codes with new and desirable parameters is an interesting research topic in coding theory and cryptography. Recently, Mesnager et.al. stated that 'constructing linear codes with good parameters from non-weakly regular bent functions is an interesting problem.' The goal of this paper is to construct linear codes with two or three weights from non-weakly regular bent functions over finite fields and analyze the minimality of the constructed linear codes. In doing so, we draw inspiration from a paper by Mesnager in which she constructed linear codes with small weights from weakly regular bent functions based on a generic construction method. First, we recall the definitions of the subsets B+(f) and B-(f) associated with a non-weakly regular bent function $f$. Next, we construct two- or three-weight linear p -ary codes on these sets using duals of the non-weakly regular bent functions that are also bent. We note that the constructed linear codes are minimal in almost all cases. Moreover, when f is a non-weakly regular bent function in a certain subclass of Generalized Maiorana-McFarland bent functions, we determine the weight distributions of the corresponding linear codes. As far as we know, the construction of linear codes from non-weakly regular bent functions over finite fields is first studied in the literature by the second author in his dissertation.

Subject Keywords

Linear p-ary codes, minimal linear codes, non-weakly regular bent functions, secret sharing schemes, weight distribut

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85123731374&origin=inward
https://hdl.handle.net/11511/97059

Journal

IEEE Transactions on Information Theory

DOI

https://doi.org/10.1109/tit.2022.3145337

Collections

Department of Mathematics, Article

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Citation Formats

F. Özbudak and R. M. Pelen, “Two or Three Weight Linear Codes from Non-Weakly Regular Bent Functions,” IEEE Transactions on Information Theory, vol. 68, no. 5, pp. 3014–3027, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85123731374&origin=inward.