1. An arithmetic encoding device for arithmetically encoding a transform coefficient obtained by performing a frequency transform on a target image of an unit region, comprising: syntax encoding circuitry that encodes a first syntax element, a second syntax element and a third syntax element that indicate the transform coefficient; wherein the first syntax element is a syntax element relating to a value whether or not the transform coefficient is equal to zero, and is encoded by using arithmetic encoding with a context, the second syntax element is a syntax element relating to a value whether or not an absolute value of the transform coefficient is larger than a predetermined value and is encoded by using arithmetic encoding with a context, the third syntax element is a syntax element relating to a value obtained by subtracting a predetermined value from the absolute value of the transform coefficient and is encoded without a context, in a case that the value of the first syntax element is zero, the syntax encoding circuitry does not encode the second syntax element, and in a case that the value of the first syntax element is not zero, the syntax encoding circuitry is capable of performing encoding functions (i) and (ii), the encoding function (i) includes encoding the second syntax element and the third syntax element, the encoding function (ii) includes not encoding the second syntax element and encoding the third syntax element, the syntax encoding circuitry refers to information indicating which of the encoding functions (i) and (ii) is to be performed, and the syntax encoding circuitry does not perform both of the encoding functions (i) and (ii) simultaneously for one transform coefficient.