DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4-Reference-Cited by-同舟云学术

DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4

Published:2022-02-01 Issue:1 Volume:30 Page:89-108
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Castillo-Guillén C. A.¹,Álvarez-García C.²

Affiliation:

1. Department of Mathematics , Universidades para el Bienestar Benito Juárez García , Tláhuac Ave 6391 , , México City , México

2. Department of Mathematics , Universidad Autónoma Metropolitana-I , San Rafael Atlixco Ave 186 , , México City , México

Abstract

Abstract A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established. Using this map the structure of DNA codes over these rings is determined, the length of the code is relatively prime to the characteristic of the residue field of the ring.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2022-0006

Reference19 articles.

1. [1] T. Abualrub, A. Ghrayeb, X. N. Zeng, Construction of cyclic codes over GF(4) for DNA computing, Journal of the Franklin Institute, 343, 448-457 (2006)

2. [2] L. Adleman, Molecular computation of solutions to combinatorial problems, Science 266, 1021-1024 (1994)10.1126/science.7973651

3. [3] C. Álvarez-García, C. A. Castillo-Guillén, DNA codes over finite local Frobenius non-chain rings of length 4, Discrete Mathematics, 341, 112404 (2021)10.1016/j.disc.2021.112404

4. [4] C. Álvarez-García, C. A. Castillo-Guillén, Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4, An. Stiint. Univ. Ovidius Constanta Ser. Mat, (to appear)

5. [5] A. Bayram, E. S. Oztas, I. Siap, Codes over 𝔽4 + v𝔽4 and some DNA applications, Designs Codes and Cryptography, 80, 379-393 (2016)