Steganographic Codes -- a New Problem of Coding Theory

— To study how to design steganographic algorithm more efficiently, a new coding problem – steganographic codes (abbreviated stego-codes) – is presented in this paper. The stego-codes are defined over the field with q(q ≥ 2) elements. Firstly a method of constructing linear stego-codes is proposed by using the direct sum of vector subspaces. And then the problem of linear stego-codes is converted to an algebraic problem by introducing the concept of tth dimension of vector space. And some bounds on the length of stego-codes are obtained, from which the maximum length embeddable (MLE) code is brought up. It is shown that there is a corresponding relation between MLE codes and perfect error-correcting codes. Furthermore the classification of all MLE codes and a lower bound on the number of binary MLE codes are obtained based on the corresponding results on perfect codes. Finally hiding redundancy is defined to value the performance of stego-codes.