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Unfortunately, the computational complexity associated with the search for d<\/jats:italic>min<\/jats:italic><\/jats:sub> and A<\/jats:italic>min<\/jats:italic><\/jats:sub> can be very high, especially for a turbo code that has high d<\/jats:italic>min<\/jats:italic><\/jats:sub> value. This paper introduces some useful properties of turbo codes that use structured interleavers together with circular encoding. These properties allow for a significant reduction of search space and thus reduce significantly the computational complexity associated with the determination of d<\/jats:italic>min<\/jats:italic><\/jats:sub> and A<\/jats:italic>min<\/jats:italic><\/jats:sub> values. \u00a9 2014 The Authors. 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