Generation of Cyclically Permutable Codes by Galois Field Fourier Transform

Cyclically permutable codes (CPCs) are important to communication networks, e.g., multiple access collision channels without feedback and frequency-hopping spread spectrum communication channels. A CPC is a block code of length n such that each codeword has full cyclic order n and all codewords are cyclically distinct. This study investigates the characteristics of finite fields to develop an efficient algorithm to find a CPC from a p-ary cyclic code, where p is a prime number. In this paper, the Galois field Fourier transform technique is used to generate a CPC of either primitive or non-primitive length.