DNA Codes with Constant GC-Content Constructed from Hadamard Matrices

Young-Sik KIM; Hosung PARK; Sang-Hyo KIM

doi:10.1587/transfun.E100.A.2408

DNA Codes with Constant GC-Content Constructed from Hadamard Matrices

Young-Sik KIM, Hosung PARK, Sang-Hyo KIM

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To construct good DNA codes based on biologically motivated constraints, it is important that they have a large minimum Hamming distance and the number of GC-content is kept constant. Also, maximizing the number of codewords in a DNA code is required for given code length, minimum Hamming distance, and number of GC-content. In most previous works on the construction of DNA codes, quaternary constant weight codes were directly used because the alphabet of DNA strands is quaternary. In this paper, we propose new coding theoretic constructions of DNA codes based on the binary Hadamard matrix from a binary sequence with ideal autocorrelation. The proposed DNA codes have a greater number of codewords than or the equal number to existing DNA codes constructed from quaternary constant weight codes. In addition, it is numerically shown that for the case of codes with length 8 or 16, the number of codewords in the proposed DNA code sets is the largest with respect to the minimum reverse complementary Hamming distances, compared to all previously known results.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.11 pp.2408-2415

Publication Date: 2017/11/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.2408

Type of Manuscript: PAPER

Category: Coding Theory

Authors

Young-Sik KIM
  Chosun University
Hosung PARK
  Chonnam National University
Sang-Hyo KIM
  Sungkyunkwan University

Keyword

binary pseudo random sequences, Hadamard matrix, DNA codes, inverse Gray mapping, minimum Hamming distance

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Young-Sik KIM, Hosung PARK, Sang-Hyo KIM, "DNA Codes with Constant GC-Content Constructed from Hadamard Matrices" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 11, pp. 2408-2415, November 2017, doi: 10.1587/transfun.E100.A.2408.
Abstract: To construct good DNA codes based on biologically motivated constraints, it is important that they have a large minimum Hamming distance and the number of GC-content is kept constant. Also, maximizing the number of codewords in a DNA code is required for given code length, minimum Hamming distance, and number of GC-content. In most previous works on the construction of DNA codes, quaternary constant weight codes were directly used because the alphabet of DNA strands is quaternary. In this paper, we propose new coding theoretic constructions of DNA codes based on the binary Hadamard matrix from a binary sequence with ideal autocorrelation. The proposed DNA codes have a greater number of codewords than or the equal number to existing DNA codes constructed from quaternary constant weight codes. In addition, it is numerically shown that for the case of codes with length 8 or 16, the number of codewords in the proposed DNA code sets is the largest with respect to the minimum reverse complementary Hamming distances, compared to all previously known results.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2408/_p

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@ARTICLE{e100-a_11_2408,
author={Young-Sik KIM, Hosung PARK, Sang-Hyo KIM, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={DNA Codes with Constant GC-Content Constructed from Hadamard Matrices},
year={2017},
volume={E100-A},
number={11},
pages={2408-2415},
abstract={To construct good DNA codes based on biologically motivated constraints, it is important that they have a large minimum Hamming distance and the number of GC-content is kept constant. Also, maximizing the number of codewords in a DNA code is required for given code length, minimum Hamming distance, and number of GC-content. In most previous works on the construction of DNA codes, quaternary constant weight codes were directly used because the alphabet of DNA strands is quaternary. In this paper, we propose new coding theoretic constructions of DNA codes based on the binary Hadamard matrix from a binary sequence with ideal autocorrelation. The proposed DNA codes have a greater number of codewords than or the equal number to existing DNA codes constructed from quaternary constant weight codes. In addition, it is numerically shown that for the case of codes with length 8 or 16, the number of codewords in the proposed DNA code sets is the largest with respect to the minimum reverse complementary Hamming distances, compared to all previously known results.},
keywords={},
doi={10.1587/transfun.E100.A.2408},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - DNA Codes with Constant GC-Content Constructed from Hadamard Matrices
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2408
EP - 2415
AU - Young-Sik KIM
AU - Hosung PARK
AU - Sang-Hyo KIM
PY - 2017
DO - 10.1587/transfun.E100.A.2408
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2017
AB - To construct good DNA codes based on biologically motivated constraints, it is important that they have a large minimum Hamming distance and the number of GC-content is kept constant. Also, maximizing the number of codewords in a DNA code is required for given code length, minimum Hamming distance, and number of GC-content. In most previous works on the construction of DNA codes, quaternary constant weight codes were directly used because the alphabet of DNA strands is quaternary. In this paper, we propose new coding theoretic constructions of DNA codes based on the binary Hadamard matrix from a binary sequence with ideal autocorrelation. The proposed DNA codes have a greater number of codewords than or the equal number to existing DNA codes constructed from quaternary constant weight codes. In addition, it is numerically shown that for the case of codes with length 8 or 16, the number of codewords in the proposed DNA code sets is the largest with respect to the minimum reverse complementary Hamming distances, compared to all previously known results.
ER -