Switching equivalence classes of perfect codes (Q1299914)

A binary 1-error correcting perfect code is called switching equivalent to the Hamming code (of the same parameters) if there is a sequence of switches (replacing a specially selected set of codewords for another set of words) which leads to the Hamming code. \textit{S. V. Avgustinovich} and \textit{F. I. Solov'eva} [Construction of perfect binary codes by the sequential translations of the \(i\)-components, Proc. Fifth Intern. Workshop ACCT, Sozopol, Bulgaria, 9-14 (1996; Zbl 0923.94035)] developed this approach and conjectured that every binary 1-error correcting perfect code is switching equivalent to a Hamming code. In the paper under review, the authors disprove this by construction of a perfect code of length 15 which can not be obtained from the Hamming code by switching.