\(\mathbb Z_2\mathbb Z_4\)-linear codes: Generator matrices and duality (Q849365)

This paper develops a general theory for \(\mathbb{Z}_2\mathbb{Z}_4\)-linear codes including generator matrices, parity-check matrices and duality. Such class of codes includes binary and quaternary linear codes generalizing them. There are some interesting classes of nonlinear binary codes that can be viewed as \(\mathbb{Z}_2\mathbb{Z}_4\)-linear codes but not as \(\mathbb{Z}_4\)-linear codes. Moreover, \(\mathbb{Z}_2\mathbb{Z}_4\) duality shows that \(\mathbb{Z}_2\mathbb{Z}_4\)-linear codes cannot be considered only as a variant of \(\mathbb{Z}_4\)-linear codes.