This article presents a new family of p-ary sequences. The proposed sequences are proved to have not only low correlation property, but also large linear span and large family size. Furthermore, it shows that the new family of sequences contains Tang’s construction as a subset if m-sequences are excluded from both constructions. This article presents a new family of p-ary sequences. The proposed sequences are proved to have not only low correlation property, but also large linear span and large family size. Furthermore, it shows that the new family of sequences contains Tang’s construction as a subset if m-sequences are excluded from both constructions.