The sextuply shortened binary Golay code is optimal

Patric R.J. Östergård

doi:10.1007/s10623-018-0532-z

The sextuply shortened binary Golay code is optimal

Patric R.J. Östergård^*

^*Tämän työn vastaava kirjoittaja

Information Theory

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

1 Sitaatiot (Scopus)

158 Lataukset (Pure)

Abstrakti

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.

Alkuperäiskieli	Englanti
Sivut	341–347
Sivumäärä	7
Julkaisu	Designs, Codes and Cryptography
Vuosikerta	87
Numero	2-3
Varhainen verkossa julkaisun päivämäärä	13 elok. 2018
DOI - pysyväislinkit	https://doi.org/10.1007/s10623-018-0532-z
Tila	Julkaistu - 15 maalisk. 2019
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

Pääsy asiakirjaan

10.1007/s10623-018-0532-z

ELEC-ostergord-golayAccepted author manuscript, 97,3 KB

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Konstruktion och klassificering av diskreta matematiska strukturer
Kokkala, J., Laaksonen, A., Östergård, P., Szollosi, F., Pöllänen, A., Heinlein, D. & Ganzhinov, M.
01/09/2015 → 31/08/2019
Projekti: Academy of Finland: Other research funding

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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 = mar,

day = "15",

doi = "10.1007/s10623-018-0532-z",

language = "English",

volume = "87",

pages = "341–347",

journal = "Designs, Codes and Cryptography",

issn = "0925-1022",

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number = "2-3",

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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

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U2 - 10.1007/s10623-018-0532-z

DO - 10.1007/s10623-018-0532-z

M3 - Article

AN - SCOPUS:85051849823

SN - 0925-1022

VL - 87

SP - 341

EP - 347

JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

IS - 2-3

ER -

The sextuply shortened binary Golay code is optimal

Abstrakti

Pääsy asiakirjaan

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Sormenjälki

Projektit

Konstruktion och klassificering av diskreta matematiska strukturer

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