I need to create possible combinations of 3 dummy variables into one categorical variable in a logistic regression using R. I made the combination manually just like the following:

new_variable_code variable_1 variable_2 variable_3

1 0 0 0

2 0 1 0

3 0 1 1

4 1 0 0

5 1 1 0

6 1 1 1

I excluded the other two options (0 0 1) and (1 0 1) because I do not need them, they are not represented by the data. I then used new_variable_code as a factor in the logistic regression along with other predictors.

My question is: Is there is any automated way to create the same new_variable_code? or even another econometric technique to encode the 3 dummy variables into 1 categorical variable inside a logistic regression model?

My objective: To understand which variable combination has the highest odds ratio on the outcome variable (along with other predictors explained in the same model).

Thank you