Abstract Algebra: Theory and Applications · Problem 8.6.16

Isomorphisms — Thomas Judson

Mathematics — Abstract Algebra · weight-distance-properties

Problem

Let

\mathbf{x}

\mathbf{y}

, and

\mathbf{z}

be binary

n

-tuples. Prove each of the following statements. ((a))

w(\mathbf{x}) = d(\mathbf{x}, \mathbf{0})

((b))

d(\mathbf{x}, \mathbf{y}) = d(\mathbf{x} + \mathbf{z}, \mathbf{y} + \mathbf{z})

((c))

d(\mathbf{x}, \mathbf{y}) = w(\mathbf{x} - \mathbf{y})