Hamming bound

A binary length-

n

M

and distance at least

2 t + 1

satisfies

M \sum_{j = 0}^{t} (j n) \leq 2^{n} .

Equality means the code is perfect.

Table of contents
- Asymptotic Hamming bound Hamming bound

Asymptotic Hamming bound ( $α_{q} (δ) \leq 1 - H_{q} (δ /2)$ )

The Hamming bound packs disjoint balls of radius approximately

δ n /2

. Taking logarithms and using the Hamming ball volume exponent gives the bound for

0 \leq δ \leq 1

.

// Target: algebra.bigb

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Asymptotic Hamming bound
Coding theory
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