A coding problem in steganography |
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Authors: | Weiming Zhang Shiqu Li |
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Institution: | (1) Department of Information Research, Information Engineering University, Zhengzhou, 450002, China;(2) School of Communication and Information Engineering, Shanghai University, Shanghai, 200076, China |
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Abstract: | 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.
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Keywords: | Steganography Stego-codes Error correcting codes Matrix encoding MLE codes Perfect codes Hiding redundancy |
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