Barcode multiplexing is a key strategy for sharing the rising capacity of next-generation sequencing devices: Synthetic DNA tags, called barcodes, are attached to natural DNA fragments within the library preparation procedure. Different libraries, can individually be labeled with barcodes for a joint sequencing procedure. A post-processing step is needed to sort the sequencing data according to their origin, utilizing these DNA labels. The final separation step is called demultiplexing and is mainly determined by the characteristics of the DNA code words used as labels. Currently, we are facing two different strategies for barcoding: One is based on the Hamming distance, the other uses the edit metric to measure distances of code words. The theory of channel coding provides well-known code constructions for Hamming metric. They provide a large number of code words with variable lengths and maximal correction capability regarding substitution errors. However, some sequencing platforms are known to have exceptional high numbers of insertion or deletion errors. Barcodes based on the edit distance can take insertion and deletion errors into account in the decoding process. Unfortunately, there is no explicit code-construction known that gives optimal codes for edit metric.