The octacode is the length-eight quaternary Preparata code. It is a linear code over the ring 
, with 256 codewords,
rather than a linear code over the finite
field 
(Maharaj 2026).
Maharaj (2026) proved that its minimum Hamming distance is four and its Hamming covering radius is two. It is therefore a quasi-perfect
code. As a covering code, it gives 
, improving the previous upper bound 352. The
covering density is 
.
Maharaj (2026) states that Claude assisted with the proof and searches and that independent
programs verified the computational claims.
