2019/03/19 by Nasreddine Benbelkacem, Benbelkacem, Nasreddine, Joaquim Borges +5 · 1 citation
Computer Science · Engineering · #94B25 #94B60 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1903.07886
openalex publication_date 2019/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space with mixed binary and quaternary alphabets. These codes are additive, in the sense that they are additive subgroups, rather than linear as they are not vector spaces over some finite field. We study the structure of these codes and we use the canonical Gray map from this space to the Hamming space to construct binary LCD codes in certain cases.