Z2Z4-ACP of codes and their applications to the noiseless two-user binary adder channel

Abstract

Linear complementary pair (abbreviated to LCP) of codes were defined by Ngo et al. in 2015, and were proved that these pairs of codes can help to improve the security of the information processed by sensitive devices, especially against so-called side-channel attacks (SCA) and fault injection attacks (FIA). In this paper, we first generalize the LCP of codes over finite fields to the additive complementary pair (ACP) of codes in the ambient space with mixed binary and quaternary alphabets. Then we provide two characterizations for the $Z_2{Z}_4$-additive codes pair $(C,D)$ to be $Z_2{Z}_4$-ACP of codes. Meanwhile, we obtain a sufficient condition for the $Z_2{Z}_4$-additive codes pair $(C,D)$ to be $Z_2{Z}_4$-ACP of codes. Under suitable conditions, we derive a necessary and sufficient condition for the Gray map Φ image of $Z_2{Z}_4$-ACP of codes $(C,D)$ to be LCP of codes over $Z_2$. Finally, we exhibit an interesting application of a special class of the $Z_2{Z}_4$-ACP of codes in coding for the two-user binary adder channel.