IEICE TRANSACTIONS on Fundamentals
A Convolution Theorem for Multiple-Valued Logic Polynomials of a Semigroup Type and Their Fast Multiplication
Summary :
In this paper, a convolution theorem which is analogous to the theorem for Fourier transform is shown among a certain type of polynomials. We establish a fast method of the multiplication in a special class of quotient rings of multivariate polynomials over q-element finite field GF(q). The polynomial which we treat is one of expressing forms of the multiple-valued logic function from the product of the semigroups in GF(q) to GF(q). Our results can be applied to the speedup of both software and hardware concerning multiple-valued Boolean logic.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.6 pp.1025-1033
- Publication Date
- 2016/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.1025
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
Authors
Hajime MATSUI
Toyota Technological Institute
Keyword
Latest Issue
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Hajime MATSUI, "A Convolution Theorem for Multiple-Valued Logic Polynomials of a Semigroup Type and Their Fast Multiplication" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 6, pp. 1025-1033, June 2016, doi: 10.1587/transfun.E99.A.1025.
Abstract: In this paper, a convolution theorem which is analogous to the theorem for Fourier transform is shown among a certain type of polynomials. We establish a fast method of the multiplication in a special class of quotient rings of multivariate polynomials over q-element finite field GF(q). The polynomial which we treat is one of expressing forms of the multiple-valued logic function from the product of the semigroups in GF(q) to GF(q). Our results can be applied to the speedup of both software and hardware concerning multiple-valued Boolean logic.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.1025/_p
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@ARTICLE{e99-a_6_1025,
author={Hajime MATSUI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Convolution Theorem for Multiple-Valued Logic Polynomials of a Semigroup Type and Their Fast Multiplication},
year={2016},
volume={E99-A},
number={6},
pages={1025-1033},
abstract={In this paper, a convolution theorem which is analogous to the theorem for Fourier transform is shown among a certain type of polynomials. We establish a fast method of the multiplication in a special class of quotient rings of multivariate polynomials over q-element finite field GF(q). The polynomial which we treat is one of expressing forms of the multiple-valued logic function from the product of the semigroups in GF(q) to GF(q). Our results can be applied to the speedup of both software and hardware concerning multiple-valued Boolean logic.},
keywords={},
doi={10.1587/transfun.E99.A.1025},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - A Convolution Theorem for Multiple-Valued Logic Polynomials of a Semigroup Type and Their Fast Multiplication
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1025
EP - 1033
AU - Hajime MATSUI
PY - 2016
DO - 10.1587/transfun.E99.A.1025
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2016
AB - In this paper, a convolution theorem which is analogous to the theorem for Fourier transform is shown among a certain type of polynomials. We establish a fast method of the multiplication in a special class of quotient rings of multivariate polynomials over q-element finite field GF(q). The polynomial which we treat is one of expressing forms of the multiple-valued logic function from the product of the semigroups in GF(q) to GF(q). Our results can be applied to the speedup of both software and hardware concerning multiple-valued Boolean logic.
ER -
English
