Back to Search
Start Over
Planar functions over fields of characteristic two
- Publication Year :
- 2013
-
Abstract
- Classical planar functions are functions from a finite field to itself and give rise to finite projective planes. They exist however only for fields of odd characteristic. We study their natural counterparts in characteristic two, which we also call planar functions. They again give rise to finite projective planes, as recently shown by the second author. We give a characterisation of planar functions in characteristic two in terms of codes over $\mathbb{Z}_4$. We then specialise to planar monomial functions $f(x)=cx^t$ and present constructions and partial results towards their classification. In particular, we show that $t=1$ is the only odd exponent for which $f(x)=cx^t$ is planar (for some nonzero $c$) over infinitely many fields. The proof techniques involve methods from algebraic geometry.<br />Comment: 23 pages, minor corrections and simplifications compared to the first version
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1301.6999
- Document Type :
- Working Paper