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A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Quasi-Cyclic Codes via Polynomial Matrices
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Summary :
A construction method of self-orthogonal and self-dual quasi-cyclic codes is shown which relies on factorization of modulus polynomials for cyclicity in this study. The smaller-size generator polynomial matrices are used instead of the generator matrices as linear codes. An algorithm based on Chinese remainder theorem finds the generator polynomial matrix on the original modulus from the ones constructed on each factor. This method enables us to efficiently construct and search these codes when factoring modulus polynomials into reciprocal polynomials.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.11 pp.1649-1653
- Publication Date
- 2021/11/01
- Publicized
- 2021/05/21
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021EAL2021
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Hajime MATSUI
Toyota Technological Institute
Keyword
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Hajime MATSUI, "A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Quasi-Cyclic Codes via Polynomial Matrices" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 11, pp. 1649-1653, November 2021, doi: 10.1587/transfun.2021EAL2021.
Abstract: A construction method of self-orthogonal and self-dual quasi-cyclic codes is shown which relies on factorization of modulus polynomials for cyclicity in this study. The smaller-size generator polynomial matrices are used instead of the generator matrices as linear codes. An algorithm based on Chinese remainder theorem finds the generator polynomial matrix on the original modulus from the ones constructed on each factor. This method enables us to efficiently construct and search these codes when factoring modulus polynomials into reciprocal polynomials.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAL2021/_p
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@ARTICLE{e104-a_11_1649,
author={Hajime MATSUI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Quasi-Cyclic Codes via Polynomial Matrices},
year={2021},
volume={E104-A},
number={11},
pages={1649-1653},
abstract={A construction method of self-orthogonal and self-dual quasi-cyclic codes is shown which relies on factorization of modulus polynomials for cyclicity in this study. The smaller-size generator polynomial matrices are used instead of the generator matrices as linear codes. An algorithm based on Chinese remainder theorem finds the generator polynomial matrix on the original modulus from the ones constructed on each factor. This method enables us to efficiently construct and search these codes when factoring modulus polynomials into reciprocal polynomials.},
keywords={},
doi={10.1587/transfun.2021EAL2021},
ISSN={1745-1337},
month={November},}
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TY - JOUR
TI - A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Quasi-Cyclic Codes via Polynomial Matrices
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1649
EP - 1653
AU - Hajime MATSUI
PY - 2021
DO - 10.1587/transfun.2021EAL2021
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2021
AB - A construction method of self-orthogonal and self-dual quasi-cyclic codes is shown which relies on factorization of modulus polynomials for cyclicity in this study. The smaller-size generator polynomial matrices are used instead of the generator matrices as linear codes. An algorithm based on Chinese remainder theorem finds the generator polynomial matrix on the original modulus from the ones constructed on each factor. This method enables us to efficiently construct and search these codes when factoring modulus polynomials into reciprocal polynomials.
ER -
English
