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A Construction of Binary Punctured Linear Codes and A Supporting Method for Best Code Search
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Reduction of redundancy and improvement of error-correcting capability are essential research themes in the coding theory. The best known codes constructed in various ways are recorded in a database maintained by Markus Grassl. In this paper, we propose an algorithm to construct the best code using punctured codes and a supporting method for constructing the best codes. First, we define a new evaluation function to determine deletion bits and propose an algorithm for constructing punctured linear codes. 27 new best codes were constructed in the proposed algorithm, and 112 new best codes were constructed by further modifying those best codes. Secondly, we evaluate the possibility of increasing the minimum distance based on the relationship between code length, information length, and minimum distance. We narrowed down the target (n, k) code to try the best code search based on the evaluation and found 28 new best codes. We also propose a method to rapidly derive the minimum weight of the modified cyclic codes. A cyclic code loses its cyclic structure when it is modified, so we extend the k-sparse algorithm to use it for modified cyclic codes as well. The extended k-sparse algorithm is used to verify our newly constructed best code.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.3 pp.372-380
- Publication Date
- 2022/03/01
- Publicized
- 2021/09/14
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021TAP0007
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding Theory
Authors
Takuya OHARA
Kobe University
Makoto TAKITA
University of Hyogo
Masakatu MORII
Kobe University
Keyword
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Takuya OHARA, Makoto TAKITA, Masakatu MORII, "A Construction of Binary Punctured Linear Codes and A Supporting Method for Best Code Search" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 3, pp. 372-380, March 2022, doi: 10.1587/transfun.2021TAP0007.
Abstract: Reduction of redundancy and improvement of error-correcting capability are essential research themes in the coding theory. The best known codes constructed in various ways are recorded in a database maintained by Markus Grassl. In this paper, we propose an algorithm to construct the best code using punctured codes and a supporting method for constructing the best codes. First, we define a new evaluation function to determine deletion bits and propose an algorithm for constructing punctured linear codes. 27 new best codes were constructed in the proposed algorithm, and 112 new best codes were constructed by further modifying those best codes. Secondly, we evaluate the possibility of increasing the minimum distance based on the relationship between code length, information length, and minimum distance. We narrowed down the target (n, k) code to try the best code search based on the evaluation and found 28 new best codes. We also propose a method to rapidly derive the minimum weight of the modified cyclic codes. A cyclic code loses its cyclic structure when it is modified, so we extend the k-sparse algorithm to use it for modified cyclic codes as well. The extended k-sparse algorithm is used to verify our newly constructed best code.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021TAP0007/_p
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@ARTICLE{e105-a_3_372,
author={Takuya OHARA, Makoto TAKITA, Masakatu MORII, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Construction of Binary Punctured Linear Codes and A Supporting Method for Best Code Search},
year={2022},
volume={E105-A},
number={3},
pages={372-380},
abstract={Reduction of redundancy and improvement of error-correcting capability are essential research themes in the coding theory. The best known codes constructed in various ways are recorded in a database maintained by Markus Grassl. In this paper, we propose an algorithm to construct the best code using punctured codes and a supporting method for constructing the best codes. First, we define a new evaluation function to determine deletion bits and propose an algorithm for constructing punctured linear codes. 27 new best codes were constructed in the proposed algorithm, and 112 new best codes were constructed by further modifying those best codes. Secondly, we evaluate the possibility of increasing the minimum distance based on the relationship between code length, information length, and minimum distance. We narrowed down the target (n, k) code to try the best code search based on the evaluation and found 28 new best codes. We also propose a method to rapidly derive the minimum weight of the modified cyclic codes. A cyclic code loses its cyclic structure when it is modified, so we extend the k-sparse algorithm to use it for modified cyclic codes as well. The extended k-sparse algorithm is used to verify our newly constructed best code.},
keywords={},
doi={10.1587/transfun.2021TAP0007},
ISSN={1745-1337},
month={March},}
Copy
TY - JOUR
TI - A Construction of Binary Punctured Linear Codes and A Supporting Method for Best Code Search
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 372
EP - 380
AU - Takuya OHARA
AU - Makoto TAKITA
AU - Masakatu MORII
PY - 2022
DO - 10.1587/transfun.2021TAP0007
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2022
AB - Reduction of redundancy and improvement of error-correcting capability are essential research themes in the coding theory. The best known codes constructed in various ways are recorded in a database maintained by Markus Grassl. In this paper, we propose an algorithm to construct the best code using punctured codes and a supporting method for constructing the best codes. First, we define a new evaluation function to determine deletion bits and propose an algorithm for constructing punctured linear codes. 27 new best codes were constructed in the proposed algorithm, and 112 new best codes were constructed by further modifying those best codes. Secondly, we evaluate the possibility of increasing the minimum distance based on the relationship between code length, information length, and minimum distance. We narrowed down the target (n, k) code to try the best code search based on the evaluation and found 28 new best codes. We also propose a method to rapidly derive the minimum weight of the modified cyclic codes. A cyclic code loses its cyclic structure when it is modified, so we extend the k-sparse algorithm to use it for modified cyclic codes as well. The extended k-sparse algorithm is used to verify our newly constructed best code.
ER -
English
