On the Theory of Cyclic Arithmetic Codes

The author proposes new cyclic arithmetic codes with a large distance, namely, $AN$-codes with
$$ A=(2^{\mathrm{lsm}(e_ip_i^{m_i-1})}-1)/B,\quad\mathrm{where}\quad B=\Pi^i_{i-1}p_i^{m_i} $$
and $e_i$. A detailed study is made of the cases $B=p_1,p_2$ и $B=p^m$, for which estimates of the arithmetic distance and efficiency of the codes are obtained.