Abstract Algebra: Theory and Applications · Problem 8.6.14

Isomorphisms — Thomas Judson

Mathematics — Abstract Algebra · coset-decoding

Problem

Let

C

be the group code in

\mathbb{Z}_2^3

defined by the codewords

(000)

and

(111)

. Compute the cosets of

C

\mathbb{Z}_2^3

. Why was there no need to specify right or left cosets? Give the single transmission error, if any, to which each coset corresponds.