On the Efficiency of Shortened Cyclic Single-Burst-Correcting Codes

Shortened cyclic codes that are capable of correcting up to a single burst of errors are considered. The efficiency of such codes has been analized by how well they approximate the Reiger bound, i.e., by the burst-correcting efficiency of the code. Although the efficiency is still an important parameter, it is shown that this one is not necessarily the most important consideration when choosing a single-burst-correcting code. It is shown that in some natural practical applications (like in a Gilbert-Elliot channel), it is more important to optimize the rate of the code with respect to its guard space, a goal closely related to the Gallager bound. The concepts of all-around, non-all around and partial all-around single-burst-correcting codes are introduced and illustrated with examples, some from existing constructions and some from new ones. Tables are presented showing that in many cases the new codes have better parameters than the existing ones for the same burst-correcting capability.