Abstract: Cayley graphs over quotients of the quaternion integers are going to be used to define a new metric over four dimensional lattices.

As in the cases of Gaussian integers [10] and Eisenstein-. Jacobi integers [11], we can define Cayley graphs over the quaternion integers or Lipschitz integers ...

This work focuses on a new class of four-dimensional signal spaces which include tori as subcases and models their signal sets through Cayley-Dickson ...

The Lipschitz metric was presented and some perfect codes over Lipschitz integers were introduced with respect to the Lipschitz metric in [11, 12]. A ...

In this paper, we study perfect codes in the Lee-Rosenbloom-Tsfasman-Jain (LRTJ) metric over the finite field Zp. We begin by deriving some new upper bounds ...

Oct 22, 2024 · The Lipschitz metric was presented and some perfect codes over Lipschitz integers were introduced with respect to the Lipschitz metric in [11, ...

This paper studies perfect codes and total perfect codes in Cayley graphs ... Perfect Codes From Cayley Graphs Over Lipschitz Integers · C. MartínezR ...

Abstract. In this paper, the goal is to obtain constacyclic codes over Lipschitz integers in terms of Lipschitz metric. A decoding procedure is proposed for ...

Jan 13, 2012 · If a code attains an upper bound (the sphere-packing bound) in a given metric, then it is called a perfect code. Perfect codes have always ...

Jun 14, 2022 · In this paper, we construct steganographic schemes explicitly from r-perfect codes on Cayley graphs over Gaussian integers, Eisenstein–Jacobi integers, and ...