On the Nonexistence of Perfect Codes in \(J(2w + p^2, w)\)

Abstract

We consider the nonexistence of \(e\)-perfect codes in the Johnson scheme \(J(n, w)\). It is proved that for each \(J(2w + 3p, w)\) for \(p\) prime and \(p \neq 2, 5\), \(J(2w + 5p, w)\) for \(p\) prime and \(p \neq 3\), and \(J(2w + p^2, w)\) for \(p\) prime, it does not contain non-trivial \(e\)-perfect codes.