Can HTML links be added to a downloaded GIF file?

I GIF format was introduced in 1987 by CompuServe in order to provide a colour image format for their file downloading areas, replacing their earlier RLE format which was black and white only. GIF became popular because it used LZW data compression, which was more efficient than the run-length encoding that formats such as PCX and MacPaint used, and fairly large images could therefore be downloaded in a reasonable amount of time, even with very slow modems.