Encoder and storage apparatus

An encoder comprising:

• a storage which stores information indicative of a generator matrix corresponding to a rank-deficient parity check matrix comprising one or more cyclic matrices or zero matrices;
• and
• a generator which carries out semi-systematic coding using the generator matrix to generate a code word, and
• wherein the generator matrix includes 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 parity check matrix, and
• at least one elementary row operation using at least one row vector contained in the non-cyclic matrix portion include an elementary row operation which increases number of nonzero elements if the elementary row operation is applied to any one row contained in the cyclic matrix portion.