Reversible $$G^k$$-codes with applications to DNA codes

Reversible Codes and Applications to DNA

The importance of DNA for living creatures is a very well known fact. Furthermore, the rich structure and knowing the role of the structure of DNA has led the researchers to the direction where the structure of DNA can be realized in computing processes and computer related technologies. Recent studies show that DNA can storage data as a big digital memory and can be a good tool for error corre...

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

A Study of Variable Length Error Correcting Codes and Reversible Variable Length Codes: Analysis and Applications

is an authentic record of my work carried out under the supervision of Prof. N. Kalyanasundaram and Prof. Bhudev Sharma. I have not submitted this work elsewhere for any other degree or diploma. I am fully responsible for the contents of my Ph.D. Thesis. is a bonafide record of her original work carried out under our supervision. This work has not been submitted elsewhere for any other degree o...

Reversible DNA codes over a family of non-chain rings

In this work we extend results introduced in [15]. Especially, we solve the reversibility problem for DNA codes over the non chain ring Rk,s = F42k [u1, . . . , us]/〈u 2 1 − u1, . . . , u 2 s − us〉. We define an automorphism θ over Rk,s which helps us both finding the idempotent decomposition of Rk,s and solving the reversibility problem via skew cyclic codes. Moreover, we introduce a generaliz...

Reversible cyclic codes over Z4