In an adaptive transform coding system and/or anadaptive transform decoding system, coding efficiency inthe case where a small number of quantized values havinglarge absolute value are present, is improved. Theadaptive transform coding system codes the small number ofquantized values having large absolute values and otherquantized values are coded separately. More particularly,the adaptive transform coding system includes a selector(6) discriminating the small number of quantized valuehaving large absolute value from other quantized value, apulse encoding means for coding the small number ofquantized values having large absolute values (8) and thepulse decoding means (16) for decoding the same, a codingmeans (7) for coding the quantized value other than thosehaving large absolute values and a decoding means (15)decoding the same, and a synthesis means (18) forsynthesizing the small number of quantized values havinglarge absolute value and other quantized values.
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