Codes Over Gaussian Integers

  title={Codes Over Gaussian Integers},
  author={K. Huber},
  journal={Proceedings. IEEE International Symposium on Information Theory},
  • K. Huber
  • Published 1993
  • Proceedings. IEEE International Symposium on Information Theory
Gaussian integers are those complex numbers which have integers as real and imaginary parts (for Gaussian integers see e.g. [2], pp.182-187). Primes of the form p s 1 mod 4 can be written in exactly one way as s,um of two squares. Hence such primes p are the product of tw3 conjugate complex Gaussian integers: p = a2+b2 = x.x* where s = a+i.b and * denotes complex conjugation x' = a i . b. Let [.] denote rounding to the closest integer and define rounding of a complex number by [ z t iy] = [z… Expand
Codes Over Rings of Algebraic Integers
We propose codes over the algebraic integers of two quadratic extensions of Q, namely, Q(i) and Q(\sqrt{-3}). The codes being proposed are designed to the Mannheim distance, although some propertiesExpand
New Coding Techniques for Codes over Gaussian Integers
Gaussian integer rings which extend the number of possible signal constellations over Gaussian integer fields, and it is demonstrated that the concept of set partitioning can be applied to Gaussian integers and enables multilevel code constructions. Expand
Multilevel Coding over Eisenstein Integers with Ternary Codes
This work introduces new signal constellations based on Eisenstein integers, i.e., the hexagonal lattice. These sets of Eisenstein integers have a cardinality which is an integer power of three. TheyExpand
New Four-Dimensional Signal Constellations From Lipschitz Integers for Transmission Over the Gaussian Channel
It is demonstrated that the concept of set partitioning can be applied to quotient rings of Lipschitz integers where the number of elements is not a prime number and it is shown that it is always possible to partition such quotients rings into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is strictly larger than in the original set. Expand
Hexagonal metric for linear codes over a finite field
  • Ying Gao
  • Mathematics, Computer Science
  • J. Syst. Sci. Complex.
  • 2011
The author presents a geometric method to construct finite signal constellations from quotient lattices associated to the rings of Eisenstein-Jacobi integers and their prime ideals and thus naturally label the constellation points by elements of a finite field. Expand
Computing Complex Convolutions Using Surrogate Fields
In this contribution we show how representations of finite fields as Gaussian integers modulo a Gaussian prime can be used for computing complex convolutions. The main idea is to switch from theExpand
Groups of complex integers used as QAM signals
  • J. Rifà
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1995
Block codes which allow error correction in a two-dimensional QAM signal space are given and are used to demodulate QAM signals in a differentially coherent detection scheme on a noisy channel. Expand
Erratum to "Lattice constellation and codes from quadratic number fields" [IEEE Trans. Inform. Theory, vol. 47, No. 4, May. 2001]
The metric defined is not true, therefore, this brings about to destroy the encoding and decoding procedures, and a proper metric is defined for some codes defined in the article and there exist some 1−error correcting perfect codes with respect to this new metric. Expand
A novice cryptosystem based on nth root of Gaussian integers
In cryptography, there are many techniques for encryption and decryption to secure communication between source and destination from different types of attacks. The Rabin cryptosystem is based onExpand
Paraunitary-Based Boolean Generator for QAM Complementary Sequences of Length $2^{K}$
A Boolean generator for a large number of standard complementary QAM sequences of length $2^{K}$ </tex-math></inline-formula> is proposed, derived from the authors’ earlier paraunitary generator, which is based on matrix multiplications. Expand