In an image coding apparatus, a transformation unit acquires a transformation coefficient by executing frequency transformation to an image. An extraction unit extracts a plurality of bits each from the transformation coefficient. A coding unit executes variable-length coding to the plurality of bits including a most significant bit, and executes fixed-length coding to the plurality of bits including a least significant bit. In an image decoding apparatus, an extraction unit extracts a plurality of bits from a code string. A decoding unit executes variable-length decoding to the plurality of bits including a most significant bit, and executes fixed-length decoding to the plurality of bits including a least significant bit. A connection unit acquires a transformation coefficient by connecting the plurality of bits each decoded. An inverse transformation unit generates the image by executing frequency-inverse transformation to the transformation coefficient.