zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Geometrically uniform codes. (English) Zbl 0734.94026
Summary: A signal space code is defined as geometrically uniform if, for any two code sequences in , there exists an isometry that maps one sequence into the other while leaving the code invariant (i.e., the symmetry group of acts transistively). Geometrical uniformity is a strong kind of symmetry that implies such properties as a) the distance profiles from code sequences in to all other code sequences are all the same, and b) all Voroni regions of code sequences in have the same shape. It is stronger than Ungerboeck-Zehavi-Wolf symmetry or Calderbank-Sloane regularity. Nonetheless, most known good classes of signal space codes are shown to be generalized coset codes, and therefore geometrically uniform, including a) lattice-type trellis codes based on lattice partitions Λ/Λ ' such that Z N /Λ/Λ ' /4Z N is a lattice partition chain, and b) PSK-type trellis codes based on up to four-way partitions of a 2 n -PSK signal set.

94B60Other types of codes
94B12Combined modulation schemes