A Novel Construction of High-Rate Unit-Memory Codes

We present a new construction of a class of unit-memory (UM) codes based on two different $(n,k)$ block codes $\mathcal C_0\neq\mathcal C_1$. This construction is aimed at optimizing not only the free distance but also the extended row distance of a code. In particular, for nonbinary alphabets, we obtain codes with free distance $d_f>d_H(\mathcal C_0)+d_H(\mathcal C_1)$, where $d_H(\mathcal C)$ denotes the minimum Hamming distance of a code $\mathcal С$. This improves the results of [1–3]. This approach mainly applies to high-rate UM codes over large alphabets. Hereby, a drastic increase of the free distance is achieved, as compared to known constructions [1, 2, 4].