I am unsure but probably it's because you can infer the remaining class. For instance, imagine you have two colors {red, blue} and you want encode that variable. One option is to create two columns, one for red and other for blue, but you could also create just n - 1 columns for example "red"; if the value is 1 then the sample is red otherwise is blue.
I am unsure but probably it's because you can infer the remaining class. For instance, imagine you have two colors {red, blue} and you want encode that variable. One option is to create two columns, one for red and other for blue, but you could also create just n - 1 columns for example "red"; if the value is 1 then the sample is red otherwise is blue.
If you review the output of the encoding, you are correct that there are 11 columns. However, only 10 of these columns contain new information that is based on a comparison between the categories in the carrier column. The 11th column, "intercept", is simply a series of 1s and will have no impact on your modelling.
As to why this 11th column exists, I'm not completely sure. Following the logic of the backward difference encoding table, perhaps it could be viewed as comparing the uppermost level with the next level up. Given that every value in the column is belongs to the uppermost level or below, all values for the encoded column in this comparison will be 1 (and the other values, if they existed, would be 0).