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When designing steganographic schemes, matrix embedding is an efficient method for increasing the embedding efficiency that is de- fined as an average number of bits embedded via per change on the cover. Random linear code-based matrix embedding can achieve high embedding efficiency but cost much in computation. In this paper, we propose a method to increase the embedding speed of matrix embedding by extending the matrix via some referential columns. Compared with the original matrix embedding, the proposed method can exponentially reduce the computational complexity for equal increment of embedding efficiency. Experimental results also show that this novel method achieves higher embedding efficiency and faster embedding speed than previous fast matrix embedding methods, and thus is more suitable for real-time steganogaphic systems.