Mersenne numbers rooted on 3 for number theoretic transforms

Number Theoretic Transforms (NTT) have been shown capable of implementing efficiently finite digital convolutions for signal processing applications in voice, video, and pattern recognition areas. In this paper the concept of Generalized Mersenne Numbers (GMN) is introduced with the goal of obtaining a new discrete transform having certain desirable properties. In particular we analyze Mersenne numbers rooted on 3, having the form m = 3^t-2. Properties and necessary conditions of the GMN are investigated. Several structural characteristics are established.