Adaptive transform coding system, adaptive transform decoding system and adaptive transform coding/decoding system

In an adaptive transform coding system and/or and adaptive transform decoding system, coding efficiency in the case where a small number of quantized values having large absolute value are present, is improved. The adaptive transform coding system codes the small number of quantized values having large absolute values and other quantized values are coded separately. More particularly, the adaptive transform coding system includes a selector (6) discriminating the small number of quantized value having large absolute value from other quantized value, a pulse coding means for coding the small number of quantized values having large absolute values (8) and the pulse decoding means (16) for decoding the same, a coding means (7) for coding the quantized value other than those having large absolute values and a decoding means (15) decoding the same, and a synthesis means (18) for synthesizing the small number of quantized values having large absolute value and other quantized values.