This HTML5 document contains 48 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dcthttp://purl.org/dc/terms/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n6http://dbpedia.org/resource/File:
n17https://global.dbpedia.org/id/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
freebasehttp://rdf.freebase.com/ns/
n9http://commons.wikimedia.org/wiki/Special:FilePath/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
wikipedia-enhttp://en.wikipedia.org/wiki/
dbphttp://dbpedia.org/property/
dbchttp://dbpedia.org/resource/Category:
provhttp://www.w3.org/ns/prov#
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Hamming_space
rdfs:label
Hamming space
rdfs:comment
In statistics and coding theory, a Hamming space (named after American mathematician Richard Hamming) is usually the set of all binary strings of length N. It is used in the theory of coding signals and transmission. More generally, a Hamming space can be defined over any alphabet (set) Q as the set of words of a fixed length N with letters from Q. If Q is a finite field, then a Hamming space over Q is an N-dimensional vector space over Q. In the typical, binary case, the field is thus GF(2) (also denoted by Z2).
foaf:depiction
n9:Hamming_distance_3_bit_binary.svg
dct:subject
dbc:Coding_theory dbc:Linear_algebra
dbo:wikiPageID
4566542
dbo:wikiPageRevisionID
1099728496
dbo:wikiPageWikiLink
dbr:Alphabet_(computer_science) n6:Hamming_distance_3_bit_binary.svg dbr:Error_detection_and_correction dbc:Coding_theory dbr:Coding_theory dbr:Statistics dbr:Submodule dbr:Finite_field dbr:Lee_distance dbr:Block_code dbr:Variable-length_code dbr:Cardinality dbr:Linear_subspace dbr:Codeword dbr:Linear_code dbc:Linear_algebra dbr:Subset dbr:Binary_string dbr:Metric_(mathematics) dbr:Hamming_code dbr:Richard_Hamming dbr:Hamming_distance dbr:Word_(formal_language_theory) dbr:Gray_isometry dbr:Ring-linear_code dbr:Code dbr:Module_(mathematics) dbr:Finite_ring dbr:GF(2) dbr:Modular_arithmetic dbr:Vector_space
owl:sameAs
wikidata:Q5645799 freebase:m.0c96xr n17:4kMhk
dbp:wikiPageUsesTemplate
dbt:Algebra-stub dbt:Reflist
dbo:thumbnail
n9:Hamming_distance_3_bit_binary.svg?width=300
dbo:abstract
In statistics and coding theory, a Hamming space (named after American mathematician Richard Hamming) is usually the set of all binary strings of length N. It is used in the theory of coding signals and transmission. More generally, a Hamming space can be defined over any alphabet (set) Q as the set of words of a fixed length N with letters from Q. If Q is a finite field, then a Hamming space over Q is an N-dimensional vector space over Q. In the typical, binary case, the field is thus GF(2) (also denoted by Z2). In coding theory, if Q has q elements, then any subset C (usually assumed of cardinality at least two) of the N-dimensional Hamming space over Q is called a q-ary code of length N; the elements of C are called codewords. In the case where C is a linear subspace of its Hamming space, it is called a linear code. A typical example of linear code is the Hamming code. Codes defined via a Hamming space necessarily have the same length for every codeword, so they are called block codes when it is necessary to distinguish them from variable-length codes that are defined by unique factorization on a monoid. The Hamming distance endows a Hamming space with a metric, which is essential in defining basic notions of coding theory such as error detecting and error correcting codes. Hamming spaces over non-field alphabets have also been considered, especially over finite rings (most notably over Z4) giving rise to modules instead of vector spaces and (identified with submodules) instead of linear codes. The typical metric used in this case the Lee distance. There exist a Gray isometry between (i.e. GF(22m)) with the Hamming distance and (also denoted as GR(4,m)) with the Lee distance.
prov:wasDerivedFrom
wikipedia-en:Hamming_space?oldid=1099728496&ns=0
dbo:wikiPageLength
4262
foaf:isPrimaryTopicOf
wikipedia-en:Hamming_space