Kovalevskaya D.I.   Solov'eva F.I.  

On the Steiner quadruple systems of small rank, embedded into perfect extended codes

Reporter: Kovalevskaya D.I.

It is well known that the set of all codewords of weight $4$ from any extended perfect code with the all-zero vector forms a Steiner quadruple system. In this paper it is shown that the Steiner quadruple system of order $2^t$ constructed by switchings from the Steiner quadruple system, corresponding to the Hamming code, is embedded into some extended perfect code constructed by switchings of $ijkl$-components from the binary extended Hamming code.

Abstracts file: KovalSol_Theses.pdf

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