The sextuply shortened binary Golay code is optimal
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Designs, Codes and Cryptography, Volume 87, issue 2-3, pp. 341–347
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.Description
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Östergård, P R J 2019, 'The sextuply shortened binary Golay code is optimal', Designs, Codes and Cryptography, vol. 87, no. 2-3, pp. 341–347. https://doi.org/10.1007/s10623-018-0532-z