any unit used in linear measurement, as the inch, foot, meter, etc. Origin of linear measure. 1885-1890. First recorded in 1885-90.
Realistically, you could put any icing you wanted on a carrot cake. The wonderful beauty of cooking is that you can make it to your liking. But, the traditional icing that most people put on carrot cake is cream cheese icing.
However, it is widely considered a Southern recipe. Traditionally, red velvet cake is iced with a French-style butter roux icing (also called ermine icing), which is very light and fluffy, but time-consuming to prepare. Cream cheese frosting and buttercream frosting are variations which have increased in popularity.