Abstract
It is proved that a binary extremal [48, 24, 12]-code can have the same cosets as a quadratic-residue code of the same dimension. Relations are given for the number of the 6-cosets of an extremal code of dimension 48 and it is proved that for such codes 66, 65, and 64 are the determining numbers of cosets.
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References
B. B. Venkov and D. M. Ivanov, “Combinatorial properties of extremal doubly even codes of length 48,” Zap. Nauchn. Sem. Leningrad. Otd. Mat. Inst. Steklov. (LOMI),175, 24–29 (1989).
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 91–100, 1991.
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Ivanov, D.M. Cosets of an extremal binary code of dimension 48. J Math Sci 63, 664–670 (1993). https://doi.org/10.1007/BF01097979
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DOI: https://doi.org/10.1007/BF01097979