A New Construction of Partial Unit Memory Codes Based on Reed–Solomon Codes

In this paper we describe a novel construction of (P)UM codes based on RS codes. These codes attain a higher increase of the extended row distance a with the same free distance as the codes derived from the original construction. The basic idea is to allow dependent rows in the generator matrices. These dependent rows are then organized in a special way. The codes that we construct have the following parameters: length $N$, rate $N-d_{\infty}/2$, free distance $d_\infty$, and $\alpha\geq d_{\infty}/8$. The construction is easily generalized. Moreover, these codes can be decoded up to half this designed extended row distance.