To reduce memory capacity and power consumption in the use of a multiplication table for efficiently realizing a Galois field operation by installing a finite multiplication table having entries sequenced in accordance with the coefficient of a divisor polynomial and repetitively calculating a partial quotient and a remainder.

A GF (28) element multiplication look up table is constructed by the selection of a column from a whole multiplication look up table and re-sequencing for efficient access. The coefficient of a polynomial expression of a Lead Solomon code generation source as the element of GF shows the held column and a memory position used for the emulation of delay sets the sequence of the columns. Thus, a complete multiplication table contains 265×265 elements. Consequently, plural multiplications can be executed by one index cycle. Thus, the product of four eight bits GF multiplications can be generated by loading 32 bits, for example.