**Abstract.**

**Error-correcting codes which are ideals in
group rings where the underlying group is metacylic and non-abelian are
examined. Such a group G(M,N,R)
is the extension of a finite cyclic group Z _{M}
by a finite cyclic group Z_{N}
and has a presentation of the form**

**where gcd(M,R)
= 1, R ^{N}
= 1 mod M, R
=/ 1. Group rings that are semi-simple, i.e.,
where the characteristic of the field does not divide the order of the
group, are considered. In all cases, the field of the group ring is of
characteristic 2,
and the order of G
is odd.**

**Algebraic analysis of the structure of the
group ring yields a unique direct sum decomposition of FG(M,
N, R) to minimal two-sided ideals (central
codes). In every case, such codes are found to be combinatorially equivalent
to abelian codes and of minimum distance that is not particulary desirable.
Certain minimal central codes decompose to a direct sum of N minimal left
ideals (left codes). This direct sum is not unique. A technique to vary
the decomposition is described.**

**Metacyclic codes that are one-sided ideals
were found to display higher minimum distances than abelian codes of comparable
length and dimension. In several cases, codes were found which have minimum
distances equal to that of the best known linear block codes of the same
length and dimension.**

**Keywords: Error-correcting codes, Algebraic
codes, Non-abelian codes, Metacyclic groups
**