Some cultures feel that having sex while the woman is menstruating is taboo, while others have a more liberal attitude, so personal attitudes will certainly impact on any decisions the pair of you will make, but from a physical point of view, there is no reason why you cannot, although it can certainly get very messy.
Some people are under the impression (again because of cultural beliefs) that a woman is ‘dirty’ or ‘unclean’ while she is having her period so there is a greater risk of infection if you were to have sex at this time, but these attitudes are misogynistic and have been brought about through ignorance and lack of understanding.
Other cultures believe that the natural rhythm of a woman’s body is more in tune with the natural cycle of the earth and so it is ridiculous to base negative superstitions around it.
Ultimately, the decision of whether or not to have sex when your partner is having her period, and whether or not to wear a condom is a decision that the two of you must make together. If you decide not to bother with the condom, you need to make the very conscious decision that you are ready to cope with the consequences should the unexpected happen, and it does result in a pregnancy.