Constant Euclidean-Norm Perfect Gaussian Integer Sequences
Abstract
This letter presents a new class of perfect Gaussian integer sequences (PGISs), called Constant Euclidean-norm PGISs, where every Gaussian integer has the same Euclidean norm. Several proposed construction methods are based on the combination of different base sequences. With the aid of Pythagorean theorem, distinct elements appearing in the base sequences result in many new families of constant Euclidean-norm PGISs with degree of freedom. Both theoretical guarantees and numerical examples of the newly proposed construction methods are provided as well.
Fields of Study & Subjects
Coding theory and cryptography
Mathematical Analysis and Transform Methods
Analytic Number Theory Research
Publication details
- Journal / source
- IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
- Volume
- E109.A
- Issue
- 8
- Pages
- 1426–1430
- Publication date
- 12 February 2026
- Language
- EN