r i x for each bit of a maximum bit length n 1 of input data so when n is large for example when n 10 000 there is a problem in that the remainder memory 11 becomes large therefore in a second embodiment of the invention the size of the remainder memory 11 can be reduced by storing a remainder value in the remainder memory 11 after every p bits with p taken to be an arbitrary constant then as shown in fig4 i which indicates the bit position is decomposed as in equation 7 where p 2 s here the necessary remainder value r i x is the remainder obtained by dividing x i by the generator polynomial g x when the quotient polynomial obtained by dividing x pn by the generator polynomial g x is expressed as q pn x and the remainder polynomial is expressed as r pn x then x i is given by the following equation so the remainder value r i x becomes equal to the remainder obtained by dividing r pn x u00b7 x k by g x therefore as shown in fig5 r pn x are correlated to a bit position n every p bits and stored as a table and a remainder is found by finding r pn x that.