On Varshamov-Tenengol'ts codes and a conjecture of L. A. Bassalygo (Q1310732)

We consider a construction problem for binary codes that correct single localized error. L. A. Bassalygo stated a conjecture that the maximum ``cardinality'' (the number of messages) of such a code is equal to the integral part of the corresponding value of the Hamming bound. Using Varshamov-Tenengolts codes, we prove that this conjecture holds true for code length \(n=p-1\), where \(p\) is a prime such that 2 is its primitive root.