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- W2797941603 abstract "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." @default.
- W2797941603 created "2018-04-24" @default.
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- W2797941603 date "2018-04-16" @default.
- W2797941603 modified "2023-10-01" @default.
- W2797941603 title "The Subfield Codes of Hyperoval and Conic codes" @default.
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- W2797941603 doi "https://doi.org/10.48550/arxiv.1804.06003" @default.
- W2797941603 hasPublicationYear "2018" @default.
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