Steganographic schemes from perfect codes on Cayley graphs

The main purpose of this paper is to give a new and general way to obtain steganographic schemes from perfect codes on Cayley graphs, motivated by the F5 algorithm based on binary Hamming codes. We obtain the steganography based on perfect Hamming codes as a special case and also give various equivalent conditions for the existence of a perfect code on a k-regular Abelian Cayley graph. Then we show that a perfect code on an Abelian Cayley graph produces a proper steganographic scheme. We further compute the various parameters for the steganographic scheme of type [n, k] over a finite field \(\mathbb {F}_q\) arising from a linear [n, n − k, d] code over \(\mathbb {F}_q\) and find also parameters for some steganographic schemes from perfect codes in k-regular Abelian Cayley graphs.