线性隐写码的性质与构造

The Properties and Constructions of Linear Steganographic Codes

本文从隐写术的安全性需求出发抽象出一个新的编码问题,称之为隐写码。利用线性空间的直和分解得到了一种线性隐写码的构造方法。通过引入线性空间t阶维数的概念将线性隐写码问题转化成了一个代数问题,从而得到了线性隐写码长度的上界,并由此定义了最大长度可嵌入码。证明了线性最大长度可嵌入码与线性完备纠错码有1-1对应关系。

A new coding problem, steganographic codes （abbreviated stego-codes）, is derived from the problem of steganography. First, the method for constructing linear stego-codes is proposed by using the direct sum of vector subspaces. Secondly, the problem of linear stego-codes is converted to an algebraic problem by introducing the tth dimension for vector spaces. The bound on the length of linear stego-codes is obtained, based on which the maximum length embeddable （MLE） codes are brought up. Furthermore, it is shown that there is a one-to-one correspondence between linear MLE codes and linear perfect error-correcting codes.