1. An image coding and decoding system which includes an image coding apparatus which codes an image signal of a picture and an image decoding apparatus which decodes a coded image signal of a picture, wherein said image coding apparatus comprises: a frequency transformation unit operable to frequency-transform a block image into a two-dimensional array of transform coefficients of a frequency component; a run-level transforming unit operable to transform the two-dimensional array of transform coefficients of a frequency component into a run value and a level value; a level value coding unit operable to code the level value; and a run value coding unit operable to code the run value, wherein the run value coding unit includes: a number calculation unit operable to calculate a number of zero-value transform coefficients with a frequency component which is not higher than a frequency component corresponding to a zero-value transform coefficient related to the run value to be coded; a table selecting unit operable to select a code table in accordance with the number of zero-value transform coefficients; and a variable length coding unit operable to variable length code the run value by using the selected code table, wherein said image decoding apparatus comprises: a receiving unit operable to receive coded data including a coded run value and a coded level value, wherein the coded run value is obtained by coding a run value which indicates the number of continuous transform coefficients, each having a zero value, and the coded level value is obtained by coding a level value which indicates a value of a transform coefficient having a non-zero value; a run value decoding unit operable to decode the coded run value to obtain a decoded run value; a level value decoding unit operable to decode the coded level value to obtain a decoded level value; and an inverse scanning unit operable to obtain a two-dimensional array of transform coefficients of the block image from the decoded level value and the decoded run value; and an inverse frequency transformation unit operable to inverse frequency transform the two-dimensional array of transform coefficients of the block image into a decoded block image, wherein the run value decoding unit includes: a number calculation unit operable to calculate a number of zero-value transform coefficients which have not been decoded; a table selecting unit operable to select a code table in accordance with the number of zero-value transform coefficients which have not been decoded; and a variable length decoding unit operable to variable length decode the coded run value from a high frequency component toward a low frequency component by using the selected code table.