Paper Info
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 \(64 \le A(18,8) \le 68\) and \(128 \le A(19,8) \le 131\). 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.
Year
DOI
Venue
2019
10.1007/s10623-018-0532-z
Designs, Codes and Cryptography
Keywords
Field
DocType
Classification, Clique, Double counting, Error-correcting code, Golay code, 94B25, 94B65, 90C27
Discrete mathematics,Combinatorics,Clique,Binary code,Error detection and correction,Binary Golay code,Mathematics,Binary number
Journal
Volume
Issue
ISSN
87
2-3
1573-7586
Citations 
PageRank 
References 
0
0.34
11
Authors
1
Name
Order
Citations
PageRank
Patric R. J. Östergård160970.61