A Hybrid Matrix–Based Encoding Scheme With Error Detection via Third-Order Recurrences

Sukran Uygun

Journal of Mathematics, 2026, vol. 2026, 1-16

Abstract: In this paper, we propose a novel encoding–decoding algorithm based on third-order linear recurrence sequences and their associated matrix representations. In particular, third-order Jacobsthal and third-order Jacobsthal–Lucas matrix sequences are combined with Padovan and Perrin matrix sequences to construct a hybrid block–based coding scheme. The plaintext is arranged into 3×3 blocks, and each block is encoded by multiplication with specially selected matrix sequences determined by a sequence tree diagram. Determinant and trace properties of the involved matrices play a fundamental role in the decoding phase. A structural performance discussion is provided analyzing encoding key domain size and algebraic robustness against representation attacks. Compared to classical Fibonacci-based coding schemes, the use of third-order recurrences and hybrid matrix selection increases structural complexity and enlarges the encoding key domain. An explicit example is provided to illustrate correctness and feasibility of the method.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/5925090.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/5925090.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5925090

DOI: 10.1155/jom/5925090

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().