Conference devoted to the 90th anniversary of Alexei A. Lyapunov

Akademgorodok, Novosibirsk, Russia, October 8-11, 2001,
(state registration number 0320300064)

Abstracts

Cybernetiks

Perfect codes with big kernel dimensions

Avgustinovich S.V., Heden O.*, Solov'eva F.I.

Sobolev Institute of Mathematics (Novosibirsk),
[*]Royal Institute of Technology (Stockholm)

Perfect codes of all admissible length n>15 with the rank r < n and the kernel of dimension k for each k in {(n-1)/2,...,U(n)} are presented (here U(n) is dimension of maximal possible kernel of a full rank perfect code of length n). Full rank perfect codes of all admissible length n>210-1 with a kernel of dimension k for each k in {(n-1)/2,...,U(n)} are given. For length 31 <= n <= 210-1 the same result for each k in {(n-1)/2,...,U(n)-2} is true.

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Note. Abstracts are published in author's edition
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