A coding problem in steganography

作者：Zhang Weiming^*; Li Shiqu

来源：Designs, Codes and Cryptography, 2008, 46(1): 67-81.

DOI：10.1007/s10623-007-9135-9

• steganography
• stego-codes
• error correcting codes
• matrix encoding
• MLE codes
• perfect codes
• hiding redundancy

To study how to design a 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. A method of constructing linear stego-codes is proposed by using the direct sum of vector subspaces. And the problem of linear stego-codes is converted to an algebraic problem by introducing the concept of the tth dimension of a vector space. Some bounds on the length of stego-codes are obtained, from which the maximum length embeddable (MLE) code arises. 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.

• 出版日期2008-1
• 单位中国人民解放军信息工程大学; 上海大学