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which PIC? 16 leds as 4x4 or 16x1 or 8x2...
If you have a program and its flicking, could you post it? so we can suggest over that? (maybe to long delay.. at 4x4 the column delay sholud be max 5ms, 1ms should be ok)
A 1/16 duty cycle is not going to be bright unless you drive the LEDs with fairly high current (60ma is often about right) Also keep your refresh rate around 50Hz per LED (800Hz for 16LEDs)
Of course the most you can get out of a single PIC pin is 25ma, you'll need a driver to get the full 60ma.