Maximal arcs and extended cyclic codes
It is proved that for every d≥2 such that d−1 divides q−1 , where q is a power of 2, there exists a Denniston maximal arc A of degree d in PG(2,q) , being invariant under a cyclic linear group that fixes one point of A and acts regularly on the set of the remaining points of A. Two alternative proofs are given, one geometric proof based on Abatangelo–Larato’s characterization of Denniston arcs, and a second coding-theoretical proof based on cyclotomy and the link between maximal arcs and two-weight codes.
Designs, Codes and Cryptography
Maximal arcs and extended cyclic codes.
Designs, Codes and Cryptography,
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© Springer Science+Business Media, LLC, part of Springer Nature 2018. Publisher’s version of record: https://doi.org/10.1007/s10623-018-0514-1