Linear codes from Denniston maximal arcs

Abstract

In this paper we construct functional codes from Denniston maximal arcs. For $$q=2^{4\ell +2}$$q=24ℓ+2 we obtain linear codes with parameters $$[(\sqrt{q}-1)(q+1),5,d]_q$$[(q-1)(q+1),5,d]q where $$\lim _{q \rightarrow +\infty } d=(\sqrt{q}-1)q-\sqrt{q}$$limq→+∞d=(q-1)q-q. We also find for $$q=16,32$$q=16,32 a number of linear codes which appear to have larger minimum distance with respect to the known codes with same length and dimension.