A coding and decoding apparatus is constructed so that the coding side transmits coded data together with identifying information for identifying the device of decoding the coded data, and the decoding side is capable of storing a number of decoding schemes so as to perform decoding based on one of the previously stored schemes. For each sensor element, the barrier blocks light that has not passed through the filter from reaching the light sensor including such that light from one sensor element is not detected by another of the sensor elements. A first conductive layer is disposed on a surface of the faceplate. The present invention greatly saves the time and cost of the device programming and testing, thus simplifying the process and saving the cost, increasing the profit. Once this extended equation is solved, the value of the payoff, the optimal hedging strategy, and the residual risk of the optimal hedge can be determined.