Strongly separable codes

Binary \(t\)-frameproof codes (\(t\)-FPCs) are used in multimedia fingerprinting schemes where the identification of authorized users taking part in the averaging collusion attack is required. In this paper, a binary strongly \(\overline{t}\)-separable code (\(\overline{t}\)-SSC) is introduced to improve such a scheme based on a binary \(t\)-FPC. A binary \(\overline{t}\)-SSC has the same traceability as a binary \(t\)-FPC but has more codewords than a binary \(t\)-FPC. A composition construction for binary \(\overline{t}\)-SSCs from \(q\)-ary \(\overline{t}\)-SSCs is described, which stimulates the research on \(q\)-ary \(\overline{t}\)-SSCs with short length. Several infinite series of optimal \(q\)-ary \(\overline{2}\)-SSCs of length \(2\) are derived from the fact that a \(q\)-ary \(\overline{2}\)-SSC of length \(2\) is equivalent to a \(q\)-ary \(\overline{2}\)-separable code of length \(2\). Combinatorial properties of \(q\)-ary \(\overline{2}\)-SSCs of length \(3\) are investigated, and a construction for \(q\)-ary \(\overline{2}\)-SSCs of length \(3\) is provided. These \(\overline{2}\)-SSCs of length \(3\) have more than \(12.5\,\%\) codewords than \(2\)-FPCs of length \(3\) could have.