Preparata Code

A Preparata code is a member of a family of nonlinear binary error-correcting codes whose quaternary versions are linear over the ring . For odd , a quaternary Preparata code has length and codewords. Its binary image under the Gray map has length and minimum Hamming distance six (Hammons et al. 1994).

Maharaj (2026) proved that , considered in the quaternary Hamming distance, has minimum distance four and covering radius two. It is a quasi-perfect code with covering density

The analogous construction for even has Hamming covering radius three. The case is the octacode. Maharaj (2026) states that Claude assisted with searches and the proof and that the computational claims were independently verified by programs.