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The subfield codes of hyperoval and conic codes.
- Source :
-
Finite Fields & Their Applications . Mar2019, Vol. 56, p308-331. 24p. - Publication Year :
- 2019
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CIPHERS
*CONIC sections
*EQUATIONS
*GEOMETRY
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 10715797
- Volume :
- 56
- Database :
- Academic Search Index
- Journal :
- Finite Fields & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 134382115
- Full Text :
- https://doi.org/10.1016/j.ffa.2018.12.006