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# even code

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.

Defines:

doubly-even code, strictly even code

Keywords:

code, even, doubly even, strictly even

Related:

LinearCode

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

94B05*no label found*

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new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier