Construction and enumeration of left dihedral codes satisfying certain duality properties

Yuan Cao, Yonglin Cao, Fanghui Ma

Let ${\mathbb{F}}_q$ be the finite field of $q$ elements and let $D_{2n}=⟨x,y\mid x^n=1,y^2=1,yxy=x^{n-1}⟩$ be the dihedral group of order $n$. Left ideals of the gr…