On the faces problem for perfect codes
نویسندگان
چکیده
Perfect 1-error correcting codes C in the hyper cube Zn 2 are considered. The possibilities for the number γ(C) of code words in a k-face γ of the hyper cube are discussed. It is shown that the possibilities for the number γ(C) depend on the dimension of the face γ, the rank of C and the dimension of the kernel of C. Especially we get an answer to a question of Sergey V. Avgustinovich whether there is a perfect code with no full (n− 1)/2-face or not.
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