Bounds on the minimum distance of the duals of BCH codes

Daniel Augot; Francoise Levy-dit-Vehel

Bounds on the minimum distance of the duals of BCH codes

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Abstract

We consider duals of BCH codes of length p^m - 1 over GF(p). A lower bound on their minimum distance is found via the adaptation of the Weil bound to cyclic codes. However, this bound is of no significance for roughly half of these codes. We partially fill this gap by giving a lower bound for an infinite class of duals of BCH codes. In the second part we present a lower bound obtained with an algorithm due to Massey and Schaub. In the case of binary codes of length 127 and 255, the results are surprisingly higher than all previously known bounds.

Original language	English
Publication status	Published - 1 Dec 1994
Event	Proceedings of the 1994 IEEE International Symposium on Information Theory - Trodheim, Norw Duration: 27 Jun 1994 → 1 Jul 1994

Conference

Conference	Proceedings of the 1994 IEEE International Symposium on Information Theory
City	Trodheim, Norw
Period	27/06/94 → 1/07/94

Cite this

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title = "Bounds on the minimum distance of the duals of BCH codes",

abstract = "We consider duals of BCH codes of length pm - 1 over GF(p). A lower bound on their minimum distance is found via the adaptation of the Weil bound to cyclic codes. However, this bound is of no significance for roughly half of these codes. We partially fill this gap by giving a lower bound for an infinite class of duals of BCH codes. In the second part we present a lower bound obtained with an algorithm due to Massey and Schaub. In the case of binary codes of length 127 and 255, the results are surprisingly higher than all previously known bounds.",

author = "Daniel Augot and Francoise Levy-dit-Vehel",

year = "1994",

month = dec,

day = "1",

language = "English",

note = "Proceedings of the 1994 IEEE International Symposium on Information Theory ; Conference date: 27-06-1994 Through 01-07-1994",

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TY - CONF

T1 - Bounds on the minimum distance of the duals of BCH codes

AU - Augot, Daniel

AU - Levy-dit-Vehel, Francoise

PY - 1994/12/1

Y1 - 1994/12/1

N2 - We consider duals of BCH codes of length pm - 1 over GF(p). A lower bound on their minimum distance is found via the adaptation of the Weil bound to cyclic codes. However, this bound is of no significance for roughly half of these codes. We partially fill this gap by giving a lower bound for an infinite class of duals of BCH codes. In the second part we present a lower bound obtained with an algorithm due to Massey and Schaub. In the case of binary codes of length 127 and 255, the results are surprisingly higher than all previously known bounds.

AB - We consider duals of BCH codes of length pm - 1 over GF(p). A lower bound on their minimum distance is found via the adaptation of the Weil bound to cyclic codes. However, this bound is of no significance for roughly half of these codes. We partially fill this gap by giving a lower bound for an infinite class of duals of BCH codes. In the second part we present a lower bound obtained with an algorithm due to Massey and Schaub. In the case of binary codes of length 127 and 255, the results are surprisingly higher than all previously known bounds.

M3 - Paper

AN - SCOPUS:0028695868

T2 - Proceedings of the 1994 IEEE International Symposium on Information Theory

Y2 - 27 June 1994 through 1 July 1994

ER -

Bounds on the minimum distance of the duals of BCH codes

Abstract

Conference

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