• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.7
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• pp.3353-3370
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• 2016

The way of combination of Product Perfect Codes (PPCs) is based on the theory of short codes constructing long codes. PPCs have larger embedding rate than Hamming codes by expending embedding columns in a coding block, and they have been proven to enhance the performance of the F₅ steganographic method. In this paper, the proposed modified product codes called MPCs are introduced as an efficient way to embed more data than PPCs by increasing 2^r₂-1-r₂ embedding columns. Unlike PPC, the generation of the check matrix H in MPC is random, and it is different from PPC. In addition a simple solving way of the linear algebraic equations is applied to figure out the problem of expending embedding columns or compensating cases. Furthermore, the MPCs over ℤ₄ have been proposed to further enhance not only the performance but also the computation speed which reaches O(n₁+σ). Finally, the proposed ℤ₄-MPC intends to maximize the embedding rate with maintaining less distortion , and the performance surpasses the existing improved product perfect codes. The performance of large embedding rate should have the significance in the high-capacity of covert communication.