Codons and Codes

Kalyan Chakraborty; Shigeru Kanemitsu; Y. Sun

doi:doi:10.11648/j.pamj.s.2015040201.15

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Codons and Codes

Kalyan Chakraborty, Shigeru Kanemitsu, Y. Sun

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 2-1)

Received: 11 December 2014 Accepted: 13 December 2014 Published: 27 December 2014

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Abstract

In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide sense due to [1] in order to understand the circular DNAs while we state rudiments of formal language theory as a means to interpret genes. We hope this will be a starter for unifying two approaches depending on the theory of codes and that of formal language.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 2-1) This article belongs to the Special Issue Abridging over Troubled Water---Scientific Foundation of Engineering Subjects
DOI	10.11648/j.pamj.s.2015040201.15
Page(s)	25-29
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Codes, Codons, Circular Codes, Linear Codes, Formal Language Theory, Regiment

References

[1]	J. Berstel and D. Perrin, Theory of codes, Pure Appl. Math. Vol. 117, Academic Press, London 1985.
[2]	C. Bonfiglio and W. Roessler, A cost optimized battery management system with active cell balancing for Lithium ion battery stacks, IEEE 2009.
[3]	A. Carbone and M. Gromov, A mathematical slices of molecular biology, Supplement to volume 88 of Gazette des Mathématiciens, French Math. Soc. (SMF), Paris 2001.
[4]	P. J. Davis and R. Hersh, Descartes' dream---The world according to mathematics, Harcourt Brace Jovanovich Publ., San Diego etc. 1986. Theo Hahn, International tables for crystallography, Reidel Publ. Co. 1983.
[5]	T. Head, Formal language theory and DNA: An analysis of the generative capacity of specific recombinant behaviors, Bull. Math. Biology 49 (1987), 737-75.
[6]	H. Kitajima and S. Kanemitsu, Math-Phys-Chem approaches to life, Intern. J. Math. Math. Sci., Volume 2012, Article ID 371825, 29 pages (doi:10.1155/2012/371825), published May 13, 2012.
[7]	A. G. Kurosh, The theory of groups I, II, Chelsea, New York 1960.
[8]	C. J. Michel and G. Pirillo, Identification of all trinucleotide circular codes coding the 20 amino acids in variant nuclear codes, Comput. Bio. Chem. 33 (2010), 122-125.
[9]	C. J. Michel, G. Pirillo and M. A. Pirillo, A classification of $20$-trinucleotide circular codes, Inf. Comput. 212 (2012), 55-63.
[10]	C. J. Michel and G. Pirillo, A permuted set of a trinucleotide circular code coding the 20 amino acids in variant nuclear codes, J. Theor. Bio. 319 (2013), 116-121.
[11]	M. Ohya and S. Matsunaga, Coding and genes, J. Electr. Inf. Comm, Soc. J74-A (1991), 1075-1084 (in Japanese).
[12]	V. Pless, Introduction to the Theory of Error-Correcting Codes, 2nd ed., Wiley, New York etc.1989.
[13]	R. Shoenheimer, The dynamic state of body constituents, Harvard Univ. Press. Massachusetts, 1942.
[14]	K. Takahashi, Descartes' dream: Cartesian product, Special issue ``Abridging over troubled water'', Pure Appl. Math. J. 2015.
[15]	Z.-Y. Zou, PSO optimization for cell-balancing charge of Lithium ion batteries, in preparation.

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APA Style

Kalyan Chakraborty, Shigeru Kanemitsu, Y. Sun. (2014). Codons and Codes. Pure and Applied Mathematics Journal, 4(2-1), 25-29. https://doi.org/10.11648/j.pamj.s.2015040201.15

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ACS Style

Kalyan Chakraborty; Shigeru Kanemitsu; Y. Sun. Codons and Codes. Pure Appl. Math. J. 2014, 4(2-1), 25-29. doi: 10.11648/j.pamj.s.2015040201.15

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AMA Style

Kalyan Chakraborty, Shigeru Kanemitsu, Y. Sun. Codons and Codes. Pure Appl Math J. 2014;4(2-1):25-29. doi: 10.11648/j.pamj.s.2015040201.15

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@article{10.11648/j.pamj.s.2015040201.15,
  author = {Kalyan Chakraborty and Shigeru Kanemitsu and Y. Sun},
  title = {Codons and Codes},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {2-1},
  pages = {25-29},
  doi = {10.11648/j.pamj.s.2015040201.15},
  url = {https://doi.org/10.11648/j.pamj.s.2015040201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040201.15},
  abstract = {In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide sense due to [1] in order to understand the circular DNAs while we state rudiments of formal language theory as a means to interpret genes. We hope this will be a starter for unifying two approaches depending on the theory of codes and that of formal language.},
 year = {2014}
}

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TY  - JOUR
T1  - Codons and Codes
AU  - Kalyan Chakraborty
AU  - Shigeru Kanemitsu
AU  - Y. Sun
Y1  - 2014/12/27
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.s.2015040201.15
DO  - 10.11648/j.pamj.s.2015040201.15
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 25
EP  - 29
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.s.2015040201.15
AB  - In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide sense due to [1] in order to understand the circular DNAs while we state rudiments of formal language theory as a means to interpret genes. We hope this will be a starter for unifying two approaches depending on the theory of codes and that of formal language.
VL  - 4
IS  - 2-1
ER  -

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Author Information

Kalyan Chakraborty

Sch. of Math.,Harish-Chandra Research Institute, Allahabad, India
Shigeru Kanemitsu

Grad. School of Adv. Tech., Kinki Univ., Iizuka, Japan
Y. Sun

Dept. of Electr. Engrg, Kyushu Inst. Techn., Tobata, Japan

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APA Style

Kalyan Chakraborty, Shigeru Kanemitsu, Y. Sun. (2014). Codons and Codes. Pure and Applied Mathematics Journal, 4(2-1), 25-29. https://doi.org/10.11648/j.pamj.s.2015040201.15

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ACS Style

Kalyan Chakraborty; Shigeru Kanemitsu; Y. Sun. Codons and Codes. Pure Appl. Math. J. 2014, 4(2-1), 25-29. doi: 10.11648/j.pamj.s.2015040201.15

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AMA Style

Kalyan Chakraborty, Shigeru Kanemitsu, Y. Sun. Codons and Codes. Pure Appl Math J. 2014;4(2-1):25-29. doi: 10.11648/j.pamj.s.2015040201.15

Copy | Download

@article{10.11648/j.pamj.s.2015040201.15,
  author = {Kalyan Chakraborty and Shigeru Kanemitsu and Y. Sun},
  title = {Codons and Codes},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {2-1},
  pages = {25-29},
  doi = {10.11648/j.pamj.s.2015040201.15},
  url = {https://doi.org/10.11648/j.pamj.s.2015040201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040201.15},
  abstract = {In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide sense due to [1] in order to understand the circular DNAs while we state rudiments of formal language theory as a means to interpret genes. We hope this will be a starter for unifying two approaches depending on the theory of codes and that of formal language.},
 year = {2014}
}

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TY  - JOUR
T1  - Codons and Codes
AU  - Kalyan Chakraborty
AU  - Shigeru Kanemitsu
AU  - Y. Sun
Y1  - 2014/12/27
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.s.2015040201.15
DO  - 10.11648/j.pamj.s.2015040201.15
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 25
EP  - 29
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.s.2015040201.15
AB  - In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide sense due to [1] in order to understand the circular DNAs while we state rudiments of formal language theory as a means to interpret genes. We hope this will be a starter for unifying two approaches depending on the theory of codes and that of formal language.
VL  - 4
IS  - 2-1
ER  -

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