On Z₂Z₂[u³]-Additive Cyclic and Complementary Dual Codes

Aydogdu
et al.
studied the standard forms of generator and parity-check matrices of
$\mathbb {Z}_{2}\mathbb {Z}_{2}[u^{3}]$
-additive codes, and presented generators of
$\mathbb {Z}_{2}\mathbb {Z}_{2}[u^{3}]$
-additive cyclic codes (Finite Fields Appl. 48: 241-260, 2017). In this paper, we investigate some other useful properties of
$\mathbb {Z}_{2}\mathbb {Z}_{2}[u^{3}]$
-additive codes, including asymptotically good
$\mathbb {Z}_{2}\mathbb {Z}_{2}[u^{3}]$
-additive cyclic codes and
$\mathbb {Z}_{2}\mathbb {Z}_{2}[u^{3}]$
-additive complementary dual codes. The present paper can be viewed as a necessary complementary part of Aydogdu’s work.