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

Date

2022-05-01

Author

Özbudak, Ferruh
Pelen, Rumi Melih

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

184
views

0
downloads

© 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

Suggestions

OpenMETU
Core

Linear codes from weakly regular plateaued functions and their secret sharing schemes Mesnager, Sihem; Özbudak, Ferruh; Sinak, Ahmet (2019-03-01) Linear codes, the most significant class of codes in coding theory, have diverse applications in secret sharing schemes, authentication codes, communication, data storage devices and consumer electronics. The main objectives of this paper are twofold: to construct three-weight linear codes from plateaued functions over finite fields, and to analyze the constructed linear codes for secret sharing schemes. To do this, we generalize the recent contribution of Mesnager given in (Cryptogr Commun 9(1):71-84, 2017...
A PUF-based lightweight group authentication and key distribution protocol Yıldız, Hüsnü; Onur, Ertan; Department of Computer Engineering (2020-9) Securing Internet of Things (IoT) applications that collect and transport sensitive data by guaranteeing authenticity, integrity, and confidentiality is a critical challenge. Reducing computation and communication overhead of security functions is also a key concern since a large number of constrained devices may take place in such applications. Our main focus in this thesis is group authentication and key management in IoT. The existing group authentication and key management protocols in the literature pe...
Differential factors and differential cryptanalysis of block cipher PRIDE Doğan, Erol; Özkan Yıldırım, Sevgi; Tezcan, Cihangir; Department of Cyber Security (2017) Today, IoT devices are used in very critical areas like payment cards, contactless keys and biometric authentication. Moreover, while the number of IoT Technologies increases, cryptographic systems that are optimized for IoT devices that require less cost, less power, and less memory are highly required in today’s industry. Therefore, in recent years several lightweight block ciphers are published to satisfy industry needs. However, there are still more work needed to be sure about the security of these blo...
A Combinatorial Methodology for Optimizing Non-Binary Graph-Based Codes: Theoretical Analysis and Applications in Data Storage Hareedy, Ahmed; Lanka, Chinmayi; Guo, Nian; Dolecek, Lara (2019-04-01) © 2018 IEEE.Non-binary (NB) low-density parity-check (LDPC) codes are graph-based codes that are increasingly being considered as a powerful error correction tool for modern dense storage devices. Optimizing NB-LDPC codes to overcome their error floor is one of the main code design challenges facing storage engineers upon deploying such codes in practice. Furthermore, the increasing levels of asymmetry incorporated by the channels underlying modern dense storage systems, e.g., multi-level Flash systems, exa...
Implementation of an Enhanced Target Localization and Identification Algorithm on a Magnetic WSN Baghaee, Sajjad; GÜRBÜZ, SEVGİ ZÜBEYDE; Uysal, Elif (2015-10-01) Wireless sensor networks (WSNs) are ubiquitous in a wide range of applications requiring the monitoring of physical and environmental variables, such as target localization and identification. One of these applications is the sensing of ferromagnetic objects. In typical applications, the area to be monitored is typically large compared to the sensing radius of each magnetic sensor. On the other hand, the RF communication radii of WSN nodes are invariably larger than the sensing radii. This makes it economic...

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.