on the $(4nu,3)$-arcs in $pg(2,q)$ and the related linear codes

In this paper, we use an irreducible plane-cubic curves in the projective plane $pg(2,q)$ to construct (k,3)-arcs of size $4nu$ where $lceil frac{q+1-2sqrt{q}}{4}rceilleqnuleqlfloor frac{q+1+2sqrt{q}}{4} rfloor$. each of these arcs gives rise to an error-correcting code that corrects the maximum possible number of errors for its length. furthermore, we discuss the completeness of each arc. the isotropy subgroup of each arc are determined. all griesmer codes that correspond to plane-cubic curves are given for $7leq qleq 37,q$ is a prime.