Integrated studies completion of BCH codes of different lengths is devoted. Most attention is paid to codes whose lengths are intermediate between primitive lengths, which are obtained by throwing in a special way from the check matrices of primitive BCH codes of a large number of columns, but with preservation of cyclical properties, which are proposed to be called non-primitive BCH codes. The properties of the named code class are systematically investigated. It is proved that, according to the variety of lengths, about a third of the non-primitive BCH codes have a code distance greater than constructive, and, therefore, they are able to correct random errors, the multiplicity of which significantly exceeds the constructive frame. Correction of such errors is called plus-decoding. It is shown that it is impossible to implement plus-decoding by known classical methods and algorithms, but only by the available and developing means of the theory of norms syndromes. Two algorithms for the implementation of plus-decoding by permutation normal methods are proposed. Non-primitive BCH-codes are promising for applications in real modern information and communication systems.