This is the 2243rd most frequent Japanese word.
行か
"行か" (ika) is a conjugated form of the verb "行く" (iku), meaning "to go."
行かない is the negative form of 'to go', showing that the action of going doesn't occur.
私は映画館へ行かない。
I do not go to the movie theater.
行かないと combines 'to not go' with 'と決めました' (decided) to express a decision regarding the action of not going.
行かないと決めました。
I decided not to go.
行かなくてもいいです expresses permission or an allowance not to perform the action of going.