Enumeration and classification of self-dual codes over finite rings with applications in cryptographic systems
Veerendra Yadavveerendra.yadav@niu.edu.inDepartment of Computer Science & EngineeringNoida International UniversityNoida, Uttar Pradesh, 203201, IndiaView full profile → , *Amruta Prasad KharadeCorresponding authoramruta.kharade@vit.eduDepartment of Engineering Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Tushatusha@quantumeducation.inQuantum University Research CenterQuantum UniversityRoorkee, Uttarakhand, 247667, India0009-0001-5904-2139View full profile → , Lokesh Ravillalokesh.ravilla.lr@gmail.comCentre for Multidisciplinary ResearchAnurag UniversityHyderabad, Telangana, 500088, India0009-0002-4910-9587View full profile → , Chetanaba G. Rajputad.admin@gokuluniversity.ac.inFaculty of Arts, Humanities and Social ScienceGokul Global UniversitySidhpur, Gujarat, 384151, India0009-0006-2894-1234View full profile → , Gourav Bathlagourav.bathla@gla.ac.inDepartment of Computer Engineering & ApplicationsGLA UniversityMathura, Uttar Pradesh, 281406, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 31 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3052
- Pages:
- 4299–4308
Abstract
Self-dual codes of finite rings have now become powerful tools of algebraic design which are important in modern cryptography. A systematic enumeration and classification plan of self-dual codes determined on different categories of finite rings is presented with a concentration on structural properties, structural equivalence and canonical forms. The paper demonstrates the generation of generators and parity-check matrices, bilinear inner product space orthogonality criteria. The module-theoretic representations and invariant-based methods aid in developing a holistic classification methodology. It is straightforward to identify individual code families and appropriateness of the code families to given cryptographic primitives like secure key exchange, error detecting and resistance to algebraic attacks. The experimental results lean more towards increased structural strength, and improved security properties than the classical field-based codes, indicating the possibility of finite ring-based self-dual codes in advanced cryptographic applications.
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References
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