Arbitrary Length Reducible and Irreducible Perfect Gaussian Integer Sequences with A Pre-Given Gaussian Integer

摘要

In this paper we will discuss two construction schemes on arbitrary length perfect Gaussian integer sequence (PGIS) with a pre-given constant. The first scheme uses geometric series, which brings reducible PGIS. We will also discuss the irreducible case and find an easy way to obtain PGIS for even length. Moreover, the same concept can be applied for some odd length N = 3p by using Ramanujan’s Sum. Concrete examples are provided.