2018/04/17 by Heng, Ziling, Ding, Cunsheng
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1804.06003
Hyperovals in \PG(2,\gf(q)) with even q are maximal arcs and an interesting research topic in finite geometries and combinatorics. Hyperovals in \PG(2,\gf(q)) are equivalent to [q+2,3,q] MDS codes over \gf(q), called hyperoval codes, in the sense that one can be constructed from the other. Ovals in \PG(2,\gf(q)) for odd q are equivalent to [q+1,3,q-1] MDS codes over \gf(q), which are called oval codes. In this paper, we investigate the binary subfield codes of two families of hyperoval codes and the p-ary subfield codes of the conic codes. The weight distributions of these subfield codes and the parameters of their duals are determined. As a byproduct, we generalize one family of the binary subfield codes to the p-ary case and obtain its weight distribution. The codes presented in this paper are optimal or almost optimal in many cases. In addition, the parameters of these binary codes and p-ary codes seem new.