Abstract Algebra: Theory and Applications · Problem 8.6.24

Isomorphisms — Thomas Judson

Mathematics — Abstract Algebra · syndrome-column-matrix

Problem

Let

\mathbf{e}_i

be the binary

n

-tuple with a 1 in the

i

th coordinate and 0's elsewhere and suppose that

H \in M_{m \times n}(\mathbb{Z}_2)

. Show that

H\mathbf{e}_i

is the

i

th column of the matrix

H