A method of decoding or encoding that includes generating a new multi-transform data structure by embedding one or more non-recursive transforms into a larger recursive transform. The method may further include receiving information regarding a target data block and determining whether to use a recursive transform or a non-recursive transform. When the determination is to use the recursive transform, the method may include generating the recursive transform using a multi-transform data structure and causing the target data block to be encoded or decoded using the generated recursive transform. If not, the method may include causing the target data block to be encoded or decoded using one of the one or more the non-recursive transforms embedded in the multi-transform data structure.