Abstract Algebra: Theory and Applications · Problem 8.6.9

Isomorphisms — Thomas Judson

Mathematics — Abstract Algebra · decoding-null-space-code

Problem

Let

C

be the code obtained from the null space of the matrix

H = \begin{pmatrix} 0 & 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 & 1 \end{pmatrix}.

Decode the message

01111 \quad 10101 \quad 01110 \quad 00011

if possible. Hint. Multiple errors occur in one of the received words.