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Steganographic Codes -- a New Problem of Coding Theory

Weiming Zhang·Shiqu Li
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Abstract

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 $q(q\ge2)$ 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 $t$th 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.

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Weiming Zhang, Shiqu Li. 2005-05-26. Steganographic Codes -- a New Problem of Coding Theory. https://arxiv.org/abs/cs/0505072

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