On the optimum distance profiles of some quasi cyclic codes

In practical wireless communication systems, optimum distance profile (ODP) is useful in the coding schemes, such as the coding of the transport format combination indicator (TFCI) in WCDMA and the channel quality indicator (CQI) in LTE. For an arbitrary binary linear code, it is hard to compute the ODP by hand. In this paper, an algorithm for determining the ODP of a given code is proposed. For example, the ODPs of some quasi cyclic codes are found and proved, and the quasi cyclic code can be fast encoded with simple shift registers. Another application of the proposed algorithm for searching codes is shown at the end of this paper.