A new lower bound for the smallest complete (k, n)-arc in $$\mathrm {PG}(2,q)$$ PG ( 2 , q )

Author:

Alabdullah S.,Hirschfeld J. W. P.

Funder

University of Sussex

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computer Science Applications

Reference15 articles.

1. Bartoli D., Marcugini S., Pambianco F.: The maximum and the minimum sizes of complete $$(n,3)$$ ( n , 3 ) -arcs in $$PG(2,16)$$ P G ( 2 , 16 ) . In: Thirteenth International Workshop on Algebraic and Combinatorial Coding Theory, Pomorie, Bulgaria, pp. 77–82, 15–21 June 2012.

2. Bartoli D., Giulietti M., Zini G.: Complete $$(k,3)$$ ( k , 3 ) -arcs from quartic curves. Des. Codes Cryptogr. 79, 487–505 (2015).

3. Bierbrauer J.: The maximal size of a 3-arc in $$\text{ PG }(2,8)$$ PG ( 2 , 8 ) . J. Comb. Math. Comb. Comput. 45, 145–161 (2003).

4. Coolsaet K., Sticker H.: A full classification of the complete $$k$$ k -arcs in $$PG(2,23)$$ P G ( 2 , 23 ) and $$PG(2,25)$$ P G ( 2 , 25 ) . J. Comb. Des. 17, 459–477 (2009).

5. Coolsaet K., Sticker H.: The complete $$k$$ k -arcs of $${\rm PG}(2,27)$$ PG ( 2 , 27 ) and $${\rm PG}(2,29)$$ PG ( 2 , 29 ) . J. Comb. Des. 19, 111–130 (2011).

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