Construction of Dual Cyclic Codes over {F}_{2}[u,v]/ < u^2, v^2 - v, uv - vu >  for DNA Computation

Manoj Kumar Singh; Abhay Kumar Singh; Narendra Kumar; Pooja Mishra; Indivar Gupta

doi:10.14429/dsj.68.12344

Manoj Kumar Singh DRDO-Scientific Analysis Group, Delhi – 110 054
Abhay Kumar Singh Indian Institute of Technology (ISM), Dhanbad – 826 004
Narendra Kumar Indian Institute of Technology (ISM), Dhanbad – 826 004
Pooja Mishra Indian Institute of Technology (ISM), Dhanbad – 826 004
Indivar Gupta DRDO-Scientific Analysis Group, Delhi – 110 054

DOI: https://doi.org/10.14429/dsj.68.12344

Keywords: Dual cyclic codes, DNA cyclic codes, Reverse constraint codes, Reverse-constraint complement codes, The GC content

Abstract

Here, we assume the construction of cyclic codes over ℜ={F}_{2}[u,v]/ < u^2, v^2 - v, uv - vu >. In particular, dual cyclic codes over ℜ= {F}_{2}[u]/ <u^2> with respect to Euclidean inner product are discussed. The cyclic dual codes over ℜ are studied with respect to DNA codes (reverse and reverse complement). Many interesting results are obtained. Some examples are also provided, which explain the main results. The GC-Content and DNA codes over ℜ are discussed. We summarise the article by giving a special DNA table.

Author Biographies

Manoj Kumar Singh, DRDO-Scientific Analysis Group, Delhi – 110 054

Mr Manoj Kumar Singh received his MSc (Mathematics) from CSJM University Kanpur. Presently, he is working as Scientist ‘D’ at SAG DRDO, Delhi. His area of research includes: Cryptology, coding theory and finite field.

Abhay Kumar Singh, Indian Institute of Technology (ISM), Dhanbad – 826 004

Dr Abhay Kumar Singh received his MSc in (Mathematics) from Institute of Science, Banaras Hindu University, Varanasi, India, in 2002, and a PhD in Algebra from IIT (BHU) Varanasi, India, in 2007. Currently working as a Senior Assistant Professor, at Indian Institute of Technology (ISM) Dhanbad, India. He has been working on the areas of theory of rings and modules, algebraic coding theory, code base cryptography, etc.

Narendra Kumar, Indian Institute of Technology (ISM), Dhanbad – 826 004

Mr. Narendra kumar received his MSc in (Mathematics) from Institute of Science, Banaras Hindu University, Varanasi, India, in 2013. Presently he is working as a senior research scholar in the Department of Applied Mathematics at IIT(ISM), Dhanbad, India. His current research area is Algebraic Coding theory.

Pooja Mishra, Indian Institute of Technology (ISM), Dhanbad – 826 004

Mrs Pooja Mishra received her MSc from Rewa University in 2003. Later on she received MTech from Amity University in 2013. Presently, she is pursuing her PhD from Indian Institute of Technology (ISM), Dhanbad. Her research interest is in information theory, cloud computing and image processing.

Indivar Gupta, DRDO-Scientific Analysis Group, Delhi – 110 054

Dr Indivar Gupta received his MSc (Mathematics) from Jiwaji University Gwalior. He obtained his PhD from Indian Institute of Technology Delhi. Presently he is working as Scientist ‘F’ at SAG DRDO, Delhi. He has published more than 20 research paper in various international journals and conferences. His area of research includes cryptology and information security, finite field and number theory.