 About 2,310 results  books.google.com Gary L. Mullen, Peter JauShyong Shiue  1993  Preview Volume 168, 1994 CODES OVER EISENSTEINJACOBI INTEGERS KLAUS
HUBER ABSTRACT. In this contribution it is shown how block codes over
Eisenstein Jacobi integers can be used for coding over twodimensional signal
space. 

 books.google.com (22) Eisenstein Unit The Eisenstein units are the EISENSTEIN INTEGERS ±1, +«,
+a>2, where Elliptic Cylindrical ... notation L(q) to refer to the closely related
function Eisenstein Jacobi Integer FUNCTION), KLEIN'S ABSOLUTE
INVARIANT, ... 

 books.google.com Gaussian integers a + bi, where a, b are integers and i2 = — 1, behave like
ordinary integers in the sense that there is ... The EisensteinJacobi integers a +
bu, where a, b are integers and u is a complex cube root of unity, a;2 + uj + 1 = 0,
also ... 

 books.google.com Interconnection networks play important roles in designing high performance computers. 

 books.google.com Case B: EinsesteinJacobi Integers In this case it is enough note that the
equation (2) is valid if we denote by [·] the operation rounding to the closest
EisensteinJacobi integer. Clearly the size of the field must be either GF(p) for p≡
1 ... 

 books.google.com For codes over hexagonal signal constellations, a similar metric can be
introduced over the set of the Eisenstein—Jacobi integers. It is useful for block
codes over tori. See, for example, IHube94b] and IHube94a]. o Generalized Lee
metric Let ... 

 books.google.com The Mannheim distance is a distance on Z[i], defined, for any two Gaussian
integers x and y, as the sum of the ... For codes over hexagonal signal
constellations a similar metric can be introduced over the set of the Eisenstein–
Jacobi integers. 

 books.google.com of certain algebraic integers such as Gauss sums to prove the law of quadratic
reciprocity occurs much earlier with Eisenstein, Jacobi, and others. Among the
various proofs of this theorem given by Gauss, the fourth (1811) and the sixth (
1818) ... 

 books.google.com Acta Crystallographica. Section A. A52, (1996) 879889 7. Huber, K.: Codes Over
Gaussian Integers. IEEE Trans, on Inf. Theory. 40, No 1, Jan. (1994) 207216 8.
Huber, K.: Codes Over EisensteinJacobi Integers. Contemporary Mathematics. 

 books.google.com However, in Eisenstein's hands, Jacobi's note would help to kindle the arithmetic
theory of complex multiplication of ... like φ(u,κ) = sinam(u,κ)(in Jacobi's notation),
admits multiplications by rational integers in the sense that, for every integer m, ... 

 