Some Optimal and Quasi-Optimal Binary Codes from Cyclic Codes over GF(2<I><SUP>m</SUP></I>)

Katsumi SAKAKIBARA; Masao KASAHARA; Yoshiharu YUBA

Some Optimal and Quasi-Optimal Binary Codes from Cyclic Codes over GF(2^m)

Katsumi SAKAKIBARA, Masao KASAHARA, Yoshiharu YUBA

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It is shown that five optimal and one quasioptimal binary codes with respect to the Griesmer bound can be obtained from cyclic codes over GF(2f^m). An [m(2^em - 1), em, 2^em-1m] code, a [3(2^2e - 1), 2e, 3・2^2e-1] code, a [2(2^2e - 1), 2, (2^2e+2 - 4)/3] code, a [3(2^2e - 1), 2, 2^2e+1 - 2] code, and a [3(2^2e - 1), 2(e+1), 3・2^2e-1 - 2] code are optimal and a [2(2^2e - 1), 2(e + 1), 2^2e - 2] code is quasi-optimal.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.10 pp.1737-1738

Publication Date: 1996/10/25

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Category: Information Theory and Coding Theory

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Katsumi SAKAKIBARA, Masao KASAHARA, Yoshiharu YUBA, "Some Optimal and Quasi-Optimal Binary Codes from Cyclic Codes over GF(2m)" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 10, pp. 1737-1738, October 1996, doi: .
Abstract: It is shown that five optimal and one quasioptimal binary codes with respect to the Griesmer bound can be obtained from cyclic codes over GF(2f^m). An [m(2^em - 1), em, 2^em-1m] code, a [3(2^2e - 1), 2e, 3・2^2e-1] code, a [2(2^2e - 1), 2, (2^2e+2 - 4)/3] code, a [3(2^2e - 1), 2, 2^2e+1 - 2] code, and a [3(2^2e - 1), 2(e+1), 3・2^2e-1 - 2] code are optimal and a [2(2^2e - 1), 2(e + 1), 2^2e - 2] code is quasi-optimal.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_10_1737/_p

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@ARTICLE{e79-a_10_1737,
author={Katsumi SAKAKIBARA, Masao KASAHARA, Yoshiharu YUBA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Some Optimal and Quasi-Optimal Binary Codes from Cyclic Codes over GF(2m)},
year={1996},
volume={E79-A},
number={10},
pages={1737-1738},
abstract={It is shown that five optimal and one quasioptimal binary codes with respect to the Griesmer bound can be obtained from cyclic codes over GF(2f^m). An [m(2^em - 1), em, 2^em-1m] code, a [3(2^2e - 1), 2e, 3・2^2e-1] code, a [2(2^2e - 1), 2, (2^2e+2 - 4)/3] code, a [3(2^2e - 1), 2, 2^2e+1 - 2] code, and a [3(2^2e - 1), 2(e+1), 3・2^2e-1 - 2] code are optimal and a [2(2^2e - 1), 2(e + 1), 2^2e - 2] code is quasi-optimal.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - Some Optimal and Quasi-Optimal Binary Codes from Cyclic Codes over GF(2m)
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1737
EP - 1738
AU - Katsumi SAKAKIBARA
AU - Masao KASAHARA
AU - Yoshiharu YUBA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1996
AB - It is shown that five optimal and one quasioptimal binary codes with respect to the Griesmer bound can be obtained from cyclic codes over GF(2f^m). An [m(2^em - 1), em, 2^em-1m] code, a [3(2^2e - 1), 2e, 3・2^2e-1] code, a [2(2^2e - 1), 2, (2^2e+2 - 4)/3] code, a [3(2^2e - 1), 2, 2^2e+1 - 2] code, and a [3(2^2e - 1), 2(e+1), 3・2^2e-1 - 2] code are optimal and a [2(2^2e - 1), 2(e + 1), 2^2e - 2] code is quasi-optimal.
ER -

Some Optimal and Quasi-Optimal Binary Codes from Cyclic Codes over GF(2^m)

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Some Optimal and Quasi-Optimal Binary Codes from Cyclic Codes over GF(2^m)