Back to Matrix Theory and Linear Algebra

Application: Error correcting codes

Constructing check and generator matrices for a Hamming code, working out its block and message lengths, and encoding messages with it.

Matrix Theory and Linear Algebra, Application: Error correcting codes

Status

FlagsLoading your progress…

1 exercise

Exercise 9.5.6

Construct check and generator matrices of a Hamming code for $r=4$ . What is the block length and message length of this code? Encode the message $00110011000~{}10100000001$ . Decode the message $001000010010000~{}010000001000001$ after correcting single-bit errors.

3.0

Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.