You can have right of residence for up to six months if you are looking for work in Sweden. To be registered in the Swedish Population Register you must have right of residence for at least one year.
You can only have right of residence (uppehållsrätt) as a job-seeker for up to six months. You can therefore not be registered in the Swedish Population Register (folkbokförd) as a job-seeker.
Job vacancies are posted in the Swedish Public Employment Service's (Arbetsförmedlingen) job database Platsbanken.
You can have right of residence if you are employed and working in Sweden, self-employed or if you are providing and performing services in Sweden.
If you do not have right of residence, you are required to have a residence permit (uppehållstillstånd) in Sweden that is valid for one year or more to be registered in the Swedish Population Register.
You can apply for a residence permit at the Swedish Migration Agency.