Construction of Cyclically Permutable Codes From Prime Length Cyclic Codes

This paper proposes a novel algorithm to find the cyclically permutable codes (CPCs) from a cyclic code. In recent years, the CPCs are increasingly important, and have been applied in the communication network and optical communication. A CPC is a block code such that each codeword has full cyclic order and all codewords are cyclically distinct. In this paper, we use the characteristics of finite fields to develop an efficient algorithm to find a CPC from a q-ary cyclic code with prime length. More precisely, we propose an effective methods to find all codewords with full cyclic order from a cyclic code for prime-primitive length and prime-nonprimitive length respectively.