Apparatus, systems and techniques based on an integer transform for encoding and decoding video or image signals, including transform of encoding and decoding of image and video signals and generation of an order-2N transform W from an order-N transform T in the field of image and video coding. For example, a retrieving unit is configured to retrieve an order-N transform T, where N is an integer; a deriving unit is configured to derive an order-2N transform W from the retrieved order-N transform T, and a transforming unit configured to generate an order-2N data Z using the derived transform W.