The sextuply shortened binary Golay code is optimal

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The sextuply shortened binary Golay code is optimal. / Östergård, Patric R.J.

julkaisussa: Designs, Codes and Cryptography, Vuosikerta 87, Nro 2-3, 15.03.2019, s. 341–347.

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Bibtex - Lataa

@article{b35a759f038544ad840d096ccbf1f2b9,
title = "The sextuply shortened binary Golay code is optimal",
abstract = "The maximum size of unrestricted binary three-error-correcting codes has been known up to the length of the binary Golay code, with two exceptions. Specifically, denoting the maximum size of an unrestricted binary code of length n and minimum distance d by A(n, d), it has been known that 64 ≤ A(18 , 8 ) ≤ 68 and 128 ≤ A(19 , 8 ) ≤ 131. In the current computer-aided study, it is shown that A(18 , 8 ) = 64 and A(19 , 8 ) = 128 , so an optimal code is obtained even after shortening the extended binary Golay code six times.",
keywords = "Classification, Clique, Double counting, Error-correcting code, Golay code, UPPER-BOUNDS, UNRESTRICTED CODES, ERROR-CORRECTING CODES",
author = "{\"O}sterg{\aa}rd, {Patric R.J.}",
year = "2019",
month = "3",
day = "15",
doi = "10.1007/s10623-018-0532-z",
language = "English",
volume = "87",
pages = "341–347",
journal = "DESIGNS CODES AND CRYPTOGRAPHY",
issn = "0925-1022",
publisher = "Springer Netherlands",
number = "2-3",

}

RIS - Lataa

TY - JOUR

T1 - The sextuply shortened binary Golay code is optimal

AU - Östergård, Patric R.J.

PY - 2019/3/15

Y1 - 2019/3/15

N2 - The maximum size of unrestricted binary three-error-correcting codes has been known up to the length of the binary Golay code, with two exceptions. Specifically, denoting the maximum size of an unrestricted binary code of length n and minimum distance d by A(n, d), it has been known that 64 ≤ A(18 , 8 ) ≤ 68 and 128 ≤ A(19 , 8 ) ≤ 131. In the current computer-aided study, it is shown that A(18 , 8 ) = 64 and A(19 , 8 ) = 128 , so an optimal code is obtained even after shortening the extended binary Golay code six times.

AB - The maximum size of unrestricted binary three-error-correcting codes has been known up to the length of the binary Golay code, with two exceptions. Specifically, denoting the maximum size of an unrestricted binary code of length n and minimum distance d by A(n, d), it has been known that 64 ≤ A(18 , 8 ) ≤ 68 and 128 ≤ A(19 , 8 ) ≤ 131. In the current computer-aided study, it is shown that A(18 , 8 ) = 64 and A(19 , 8 ) = 128 , so an optimal code is obtained even after shortening the extended binary Golay code six times.

KW - Classification

KW - Clique

KW - Double counting

KW - Error-correcting code

KW - Golay code

KW - UPPER-BOUNDS

KW - UNRESTRICTED CODES

KW - ERROR-CORRECTING CODES

UR - http://www.scopus.com/inward/record.url?scp=85051849823&partnerID=8YFLogxK

U2 - 10.1007/s10623-018-0532-z

DO - 10.1007/s10623-018-0532-z

M3 - Article

VL - 87

SP - 341

EP - 347

JO - DESIGNS CODES AND CRYPTOGRAPHY

JF - DESIGNS CODES AND CRYPTOGRAPHY

SN - 0925-1022

IS - 2-3

ER -

ID: 27672726