Encoder, decoder, encoding method, and decoding method

A decoder comprising:

• circuitry;
• and
• memory coupled to the circuitry, wherein
• using the memory, the circuitry, in operation:
• performs an up-conversion and a down-conversion on a first quantization matrix to generate a second quantization matrix, the first quantization matrix having a first number of rows and a first number of columns equal to the first number of rows to form a square matrix, the second quantization matrix having a second number of rows and a second number of columns different from the second number of rows to form a rectangular matrix;
• and
• inverse quantizes quantized coefficients of a current block using the second quantization matrix, wherein
• the up-conversion is performed on the first quantization matrix in a first direction such that one of the second number of rows and the second number of columns is larger than the first number of rows, without up-conversion being performed on the first quantization matrix in a second direction that is different from the first direction;
• and
• the down-conversion is performed on the first quantization matrix in the second direction such that the other of the second number of rows and the second number of columns is smaller than the first number of rows, without down-conversion being performed on the first quantization matrix in the first direction.