PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (236)
Orphanage
Unclass'd (1)
Unproven (540)
Corrections (46)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Copyright
About
Owner confidence rating: Medium Entry average rating: No information on entry rating
even code (Definition)

A binary code is called even if the Hamming weight of all its codewords is even. Furthermore, a binary code is called doubly-even if the Hamming weight of all its codewords is divisible by $4$ An even code which is not doubly-even is said to be strictly even.

Examples of doubly-even codes are the extended binary Hamming code of block length $8$ and the extended binary Golay code of block length $24$ These two codes are, in addition, self-dual.



"even code" is owned by GrafZahl.
(view preamble | get metadata)

View style:

See Also: linear code

Also defines:  doubly-even code, strictly even code
Keywords:  code, even, doubly even, strictly even
Log in to rate this entry.
(view current ratings)

Cross-references: self-dual, addition, extended binary golay code, block length, code, binary, strictly, divisible, Hamming weight, even, binary code
There is 1 reference to this entry.

This is version 1 of even code, born on 2005-05-12.
Object id is 7047, canonical name is EvenCode.
Accessed 2771 times total.

Classification:
AMS MSC: 94B05 (Information and communication, circuits :: Theory of error-correcting codes and error-detecting codes :: Linear codes, general)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)