Good codes from metacyclic groups II

In this paper, we consider semisimple group algebras [Formula: see text] of split metacyclic groups over finite fields. We construct left codes in [Formula: see text] in the case when the order [Formula: see text] is [Formula: see text], where [Formula: see text] and [Formula: see text] are different primes such that [Formula: see text] extend the construction described in a previous paper, determine their dual codes and find some good codes.

Bound on the diameter of metacyclic groups

Let [Formula: see text] be the split metacyclic group, where [Formula: see text] is a unit modulo [Formula: see text]. We derive an upper bound for the diameter of [Formula: see text] using an arithmetic parameter called the weight, which depends on [Formula: see text], [Formula: see text], and the order of [Formula: see text]. As an application, we show how this would determine a bound on the diameter of an arbitrary metacyclic group.

Directed Strongly Regular Cayley Graphs over Metacyclic Groups of Order 4n

We construct several new families of directed strongly regular Cayley graphs (DSRCGs) over the metacyclic group M 4 n = ⟨ a , b | a n = b 4 = 1 , b − 1 a b = a − 1 ⟩ , some of which generalize those earlier constructions. For a prime p and a positive integer α > 1 , for some cases, we characterize the DSRCGs over M 4 p α .