Maximal arcs and extended cyclic codes

Authors

Stefaan DeWinter, Michigan Technological UniversityFollow
Cunsheng Ding, Hong Kong University of Science and Technology
Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

4-2019

Abstract

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.

Publisher's Statement

© Springer Science+Business Media, LLC, part of Springer Nature 2018. Publisher’s version of record: https://doi.org/10.1007/s10623-018-0514-1

Publication Title

Designs, Codes and Cryptography

Recommended Citation

DeWinter, S., Ding, C., & Tonchev, V. (2019). Maximal arcs and extended cyclic codes. Designs, Codes and Cryptography, 87(4), 807-816. http://doi.org/10.1007/s10623-018-0514-1
Retrieved from: https://digitalcommons.mtu.edu/math-fp/70