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On intersections of perfect binary codes. (English) Zbl 1100.94027
Summary: Intersections of perfect 1-error correcting binary codes are studied. It is proved that for any two integers $$k_1$$ and $$k_2$$ satisfying $$1\leq k_i \leq 2^{(n+1)/2-\log(n+1)}$$, $$i=1,2$$ there exist perfect codes $$C_1$$ and $$C_2$$, both of length $$n=2^m-1$$, $$m\geq 4$$, with $$|C_1\cap C_2|= 2k_1k_2$$.

##### MSC:
 94B65 Bounds on codes 94B60 Other types of codes
nonlinear codes