1 research outputs found
Constructions of Self-Dual and Formally Self-Dual Codes from Group Rings
We give constructions of self-dual and formally self-dual codes from group
rings where the ring is a finite commutative Frobenius ring. We improve the
existing construction given in \cite{Hurley1} by showing that one of the
conditions given in the theorem is unnecessary and moreover it restricts the
number of self-dual codes obtained by the construction. We show that several of
the standard constructions of self-dual codes are found within our general
framework. We prove that our constructed codes correspond to ideals in the
group ring and as such must have an automorphism group that contains
as a subgroup. We also prove that a common construction technique for producing
self-dual codes cannot produce the putative Type~II code.
Additionally, we show precisely which groups can be used to construct the
extremal Type II codes over length 24 and 48