Encoder and storage device

According to an embodiment, an encoder has a storage and a generator. The storage stores information indicative of a generator matrix corresponding to a partial parity check matrix in a rank-deficient parity check matrix including a lower triangular matrix and one or more cyclic matrices or zero matrices, the partial parity check matrix including rows different from rows of the lower triangular matrix. The generator carries out semi-systematic coding using the generator matrix to generate a portion of code word. The generator matrix has a cyclic matrix portion with one or more cyclic matrices and a non-cyclic matrix portion with rows number of which is equal to a degree of rank deficiency in the partial parity check matrix.