Abstract: One of the key problems in DNA computation is the design of large and reliable codes. Due to the biological and chemical restrictions, DNA codes need to satisfy certain constraints. Here, we provide an algebraic procedure to construct DNA codes by using homomorphism of groups. The construction procedure is used to determine mutation. © 2014, © Taru Publications.

Selvakumar R

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Unconventional construction of DNA codes: Group Homomorphism

Journal of Discrete Mathematical Sciences and Cryptography

Low Density Parity Check (LDPC) codes have been of great interest to researchers due to its low complexity in encoding as well as decoding. Since the introduction of Turbo codes in 1993, importance of LDPC codes has been widely explored. Various techniques have been introduced for encoding and decoding of low density parity check codes based on algebraic structures, codes on graphs, etc. In this paper, a new method of constructing binary and nonbinary LDPC-like codes from Kernel codes defined over groups is discussed. Also, we show that constructions of binary and nonbinary LDPC-like codes are particular cases of our proposed method. © Springer India 2016.

Advances in Intelligent Systems and Computing Proceedings of the Second International Conference on Computer and Communication Technologies

Construction of Binary and Nonbinary LDPC-like Codes from Kernel Codes

Forney's representation of Trellis code received wide attention by researchers and engineers with its simplicity in representing codes and elegant nature to analyze codes with sys- tem theoretic properties, graph theoretic properties with efficient encoding and decoding procedures. In this paper, we consider the connected graph nature of trellis and propose security feature over Trellis using fundamental cut-set and fundamental circuits principle. We use the graph theoretic approach, by generating limited spanning trees of trellis, fundamental cut-sets and fundamental circuits, private key cryptosystem is defined in which fundamental cut-set acts as a key to encrypt and decrypt. We have used a class of group codes called Kernel codes and its trellis, to show that private key cryptosystem can be used over Trellis and fundamental cut-set acts as a key to encrypt and decrypt message at sender and receiver respectively. © 2015 IEEE.

2015 International Conference on Smart Technologies and Management for Computing, Communication, Controls, Energy and Materials (ICSTM)

Secure communication over Trellis: Graph theoretic approach

Trellis representation of codes helps in analyzing and understanding the nature of the codes. Trellis has the connected graph nature where all paths from the 'root' vertex to 'goal' vertex forms the codewords. Efficient encoding and decoding algorithms are existing for communication over trellis. In the conventional communication system, Trellis is constructed for the encoded message at the sender and the algorithm such as Viterbi is used to decode the encoded message at the receiver. Any receiver with such decoding mechanism can be able to decode the message, which gives the chance for the intruder to get the message making the communication insecure. In this paper we propose a reliable and secure communication system which provides reliability by the Error Correction Techniques and Security by the graph based Cryptosystem. Using such system intruder's access to the informa- tion can be avoided and also if any errors occurred during transmission over noisy channel can be corrected. We have used Kernel codes and it's Trellis representation to demonstrate the construction of reliable and secure cryptosystem. © 2015 The Authors.

Journal	Journal of Discrete Mathematical Sciences and Cryptography
Publisher	Informa UK Limited
ISSN	0972-0529
Open Access	0