Abstract Algebra: Theory and Applications · Problem 8.5.4

Isomorphisms — Thomas Judson

Mathematics — Abstract Algebra · parity-check-matrix-syndrome

Problem

Suppose a linear code

C

is created as the null space of the parity-check matrix

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

Then

x = 11100

is not a codeword. Describe a computation, and give the result of that computation, which verifies that

x

is not a codeword of the code

C