Abstract
We suggest the following construction of codes. In the Hamming code H n , we first choose a collection of~ m disjoint i q -components, q=1,…, m. Then, for each q, we inverse the i q th coordinate in all vectors of the i q -component of this collection. The family of perfect codes obtained in such a way contains Vasil'ev's codes and also a number of other codes, possessing various interesting properties: the nonsystematic codes, the codes of full rank, and the codes with trivial automorphism group. In the present article we enumerate all perfect codes of length 15 obtained by means of such a construction from the Hamming code H 15; their number is shown to be equal to 131224492.
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