Encoder, decoder, encoding method, and decoding method

A decoder, comprising:

• circuitry;
• and
• memory coupled to the circuitry,
• wherein the circuitry, in operation:
• determines an inverse transform process to be performed on prediction residuals of a current block, the inverse transform process selectively including an inverse orthogonal transform and selectively including an inverse secondary transform, the inverse orthogonal transform producing transform coefficients of the current block, the inverse secondary transform producing inverse secondary transform coefficients of the current block;
• and
• performs either a first inverse quantization process or a second inverse quantization process on the current block based on the determined inverse transform process, wherein
• the first inverse quantization process is performed on the current block in both of a first case where both the inverse orthogonal transform and the inverse secondary transform are skipped for the current block and a second case where both the inverse orthogonal transform and the inverse secondary transform are performed on the current block, the first inverse quantization process not using an inverse quantization matrix, and
• the second inverse quantization process is performed on the current block in a case where the inverse orthogonal transform is performed and the inverse secondary transform is not performed on the current block, the second inverse quantization process using a first inverse quantization matrix, the first inverse quantization matrix generated by performing an up-conversion and a down-conversion on a second inverse quantization matrix.

An encoding method, comprising:

• determining a transform process to be performed on prediction residuals of a current block, the transform process selectively including an orthogonal transform and selectively including a secondary transform, the orthogonal transform producing transform coefficients of the current block, the secondary transform producing secondary transform coefficients of the current block;
• and
• performing either a first quantization process or a second quantization process on the current block based on the determined transform process, wherein
• the first quantization process is performed on the current block in both of a first case where both the orthogonal transform and the secondary transform are skipped for the current block and a second case where both the orthogonal transform and the secondary transform are performed on the current block, the first quantization process not using a quantization matrix, and
• the second quantization process is performed on the current block in a case where the orthogonal transform is performed and the secondary transform is not performed on the current block, the second quantization process using a first quantization matrix, the first quantization matrix generated by performing an up-conversion and a down-conversion on a second quantization matrix.

A decoding method, comprising:

• determining an inverse transform process to be performed on prediction residuals of a current block, the inverse transform process selectively including an inverse orthogonal transform and selectively including an inverse secondary transform, the inverse orthogonal transform producing transform coefficients of the current block, the inverse secondary transform producing inverse secondary transform coefficients of the current block;
• and
• performing either a first inverse quantization process or a second inverse quantization process on the current block based on the determined inverse transform process, wherein
• the first inverse quantization process is performed on the current block in both of a first case where both the inverse orthogonal transform and the inverse secondary transform are skipped for the current block and a second case where both the inverse orthogonal transform and the inverse secondary transform are performed on the current block, the first inverse quantization process not using a quantization matrix, and
• the second inverse quantization process is performed on the current block in a case where the inverse orthogonal transform is performed and the inverse secondary transform is not performed on the current block, the second inverse quantization process using a first quantization matrix, the first quantization matrix generated by performing an up-conversion and a down-conversion on a second quantization matrix.