In the adaptive transform coding system and / or the adaptive transform decoding system, the coding efficiency when there are a small number of quantization values having a large absolute value is improved. The adaptive transform coding system individually codes a small number of quantized values with large absolute values, and other quantized values are coded. In particular, the adaptive transform coding system decodes a selector unit 6 for discriminating a small number of quantized values having a large absolute value from other quantized values, a pulse coding unit 8 for coding a small number of quantized values having a large absolute value, and a quantized value. A pulse decoding unit 16 for coding, a coding unit 7 for coding a quantization value different from a large absolute value, and a decoding unit 15 for decoding a quantization value, and a small number of quantization values and other quantization having a large absolute value. And a comprehensive unit 18 for synthesizing the values.
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