The invention relates to an apparatus and method for encoding data and decoding data. For example, the invention is dimension Data Length Codeword of Encoding apparatus 102, which encodes into Based on, Data using code It includes a processor (102a) configured to encode a code, The length And minimum distance Have, And Is an integer, ego, The code of Set of freeze bit indices, if If it is, This, And if If it is, This, Is the expression Is the limiting matrix given by the solution of The heat Matrix with last non-zero element in Is the index of the row, Is the precoding matrix, The Is a matrix defined based on Silver matrix With his own Represents times Kronecker product.
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