Quaternary constructions for the binary single-error-correcting codes of Julin, Best and others (Q1321554)

Certain nonlinear binary single-error-correcting codes of Julin, Best and others are shown to have simple descriptions as codes over the ring of integers modulo 4. The binary codes are constructed from the codes over \(\mathbb{Z}_ 4\) by the map: \(\varphi\): \(0\mapsto 00\), \(1\mapsto 01\), \(2\mapsto 11\), \(3\mapsto 10\). Sphere packings from the lattices derived from the codes constructed are also considered.