A Practical Method for Arithmetic Computations in a Finite Field by Using Log Tables

Kyoki IMAMURA

A Practical Method for Arithmetic Computations in a Finite Field by Using Log Tables

Kyoki IMAMURA

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A simple and practical method for arithmetic computations in a finite field GF (pⁿ) is presented. Since number of elements of GF (pⁿ) is pⁿ, the method uses representation of a field element as an integer modulo pⁿ. The method also uses log and antilog tables. Only one n-th of memories are required to store the log and antilog tables of this paper in comparison with ordinary log and antilog tables. It is not necessary to compute by using vectors. It is also shown that Zech's logarithm defined by Conway can be easily computed by using the log and antilog tables of this paper. The results of this paper are useful for decoding error-correcting cyclic codes.

Publication: IEICE TRANSACTIONS on transactions Vol.E63-E No.2 pp.93-97

Publication Date: 1980/02/25

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Type of Manuscript: PAPER

Category: Electromagnetic Theory, Mathematics, Pyhsics

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Kyoki IMAMURA

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Kyoki IMAMURA, "A Practical Method for Arithmetic Computations in a Finite Field by Using Log Tables" in IEICE TRANSACTIONS on transactions, vol. E63-E, no. 2, pp. 93-97, February 1980, doi: .
Abstract: A simple and practical method for arithmetic computations in a finite field GF (pⁿ) is presented. Since number of elements of GF (pⁿ) is pⁿ, the method uses representation of a field element as an integer modulo pⁿ. The method also uses log and antilog tables. Only one n-th of memories are required to store the log and antilog tables of this paper in comparison with ordinary log and antilog tables. It is not necessary to compute by using vectors. It is also shown that Zech's logarithm defined by Conway can be easily computed by using the log and antilog tables of this paper. The results of this paper are useful for decoding error-correcting cyclic codes.
URL: https://globals.ieice.org/en_transactions/transactions/10.1587/e63-e_2_93/_p

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@ARTICLE{e63-e_2_93,
author={Kyoki IMAMURA, },
journal={IEICE TRANSACTIONS on transactions},
title={A Practical Method for Arithmetic Computations in a Finite Field by Using Log Tables},
year={1980},
volume={E63-E},
number={2},
pages={93-97},
abstract={A simple and practical method for arithmetic computations in a finite field GF (pⁿ) is presented. Since number of elements of GF (pⁿ) is pⁿ, the method uses representation of a field element as an integer modulo pⁿ. The method also uses log and antilog tables. Only one n-th of memories are required to store the log and antilog tables of this paper in comparison with ordinary log and antilog tables. It is not necessary to compute by using vectors. It is also shown that Zech's logarithm defined by Conway can be easily computed by using the log and antilog tables of this paper. The results of this paper are useful for decoding error-correcting cyclic codes.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - A Practical Method for Arithmetic Computations in a Finite Field by Using Log Tables
T2 - IEICE TRANSACTIONS on transactions
SP - 93
EP - 97
AU - Kyoki IMAMURA
PY - 1980
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E63-E
IS - 2
JA - IEICE TRANSACTIONS on transactions
Y1 - February 1980
AB - A simple and practical method for arithmetic computations in a finite field GF (pⁿ) is presented. Since number of elements of GF (pⁿ) is pⁿ, the method uses representation of a field element as an integer modulo pⁿ. The method also uses log and antilog tables. Only one n-th of memories are required to store the log and antilog tables of this paper in comparison with ordinary log and antilog tables. It is not necessary to compute by using vectors. It is also shown that Zech's logarithm defined by Conway can be easily computed by using the log and antilog tables of this paper. The results of this paper are useful for decoding error-correcting cyclic codes.
ER -