Abstract Algebra: Theory and Applications · Problem 8.6.2

Isomorphisms — Thomas Judson

Mathematics — Abstract Algebra · group-codes

Problem

Without doing any addition, explain why the following set of 4-tuples in

\mathbb{Z}_2^4

cannot be a group code.

(0110) \quad (1001) \quad (1010) \quad (1100)

Hint. This cannot be a group code since

(0000) \notin C