An encoder includes memory and circuitry accessible to the memory. The circuitry accessible to the memory: switches whether or not to apply arithmetic encoding to a binary data string in which image information has been binarized; binarizes frequency transform coefficient information according to different binarization formats between when arithmetic encoding is applied to the binary data string and when arithmetic encoding is not applied to the binary data string; and binarizes a part or the entirety of prediction parameter information according to a binarization format which is common between when arithmetic encoding is applied to the binary data string and when arithmetic encoding is not applied to the binary data string.