Integer codes are defined by error-correcting codes over integers modulo a fixed positive integer. In this paper, we show that the construction of integer codes can be reduced into the cases of prime-power moduli. We can efficiently search integer codes with small prime-power moduli and can construct target integer codes with a large composite-number modulus. Moreover, we also show that this prime-factorization reduction is useful for the construction of self-orthogonal and self-dual integer codes, i.e., these properties in the prime-power moduli are preserved in the composite-number modulus. Numerical examples of integer codes and generator matrices demonstrate these facts and processes.
Hajime MATSUI
Toyota Technological Institute
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Hajime MATSUI, "A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Integer Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 11, pp. 1952-1956, November 2018, doi: 10.1587/transfun.E101.A.1952.
Abstract: Integer codes are defined by error-correcting codes over integers modulo a fixed positive integer. In this paper, we show that the construction of integer codes can be reduced into the cases of prime-power moduli. We can efficiently search integer codes with small prime-power moduli and can construct target integer codes with a large composite-number modulus. Moreover, we also show that this prime-factorization reduction is useful for the construction of self-orthogonal and self-dual integer codes, i.e., these properties in the prime-power moduli are preserved in the composite-number modulus. Numerical examples of integer codes and generator matrices demonstrate these facts and processes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1952/_p
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@ARTICLE{e101-a_11_1952,
author={Hajime MATSUI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Integer Codes},
year={2018},
volume={E101-A},
number={11},
pages={1952-1956},
abstract={Integer codes are defined by error-correcting codes over integers modulo a fixed positive integer. In this paper, we show that the construction of integer codes can be reduced into the cases of prime-power moduli. We can efficiently search integer codes with small prime-power moduli and can construct target integer codes with a large composite-number modulus. Moreover, we also show that this prime-factorization reduction is useful for the construction of self-orthogonal and self-dual integer codes, i.e., these properties in the prime-power moduli are preserved in the composite-number modulus. Numerical examples of integer codes and generator matrices demonstrate these facts and processes.},
keywords={},
doi={10.1587/transfun.E101.A.1952},
ISSN={1745-1337},
month={November},}
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TY - JOUR
TI - A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Integer Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1952
EP - 1956
AU - Hajime MATSUI
PY - 2018
DO - 10.1587/transfun.E101.A.1952
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2018
AB - Integer codes are defined by error-correcting codes over integers modulo a fixed positive integer. In this paper, we show that the construction of integer codes can be reduced into the cases of prime-power moduli. We can efficiently search integer codes with small prime-power moduli and can construct target integer codes with a large composite-number modulus. Moreover, we also show that this prime-factorization reduction is useful for the construction of self-orthogonal and self-dual integer codes, i.e., these properties in the prime-power moduli are preserved in the composite-number modulus. Numerical examples of integer codes and generator matrices demonstrate these facts and processes.
ER -