On some self-dual codes and unimodular lattices in dimension 48
European Journal of Combinatorics
New constructions of optimal self-dual binary codes of length 54
Designs, Codes and Cryptography
Designs from subcode supports of linear codes
Designs, Codes and Cryptography
A group ring construction of the [48,24,12] type II linear block code
Designs, Codes and Cryptography
The binary extremal self-dual codes of lengths 38 and 40
Designs, Codes and Cryptography
On the classification and enumeration of self-dual codes
Finite Fields and Their Applications
| Hi-index | 754.84 |
An extremal self-dual doubly-even binary (n,k,d) code has a minimum weight d=4└n/24┘+4. Of such codes with length divisible by 24, the Golay code is the only (24,12,8) code, the extended quadratic residue code is the only known (48,24,12) code, and there is no known (72,36,16) code. One may partition the search for a (48,24,12) self-dual doubly-even code into three cases. A previous search assuming one of the cases found only the extended quadratic residue code. We examine the remaining two cases. Separate searches assuming each of the remaining cases found no codes and thus the extended quadratic residue code is the only doubly-even self-dual (48,24,12) code.