Fractional Dimensional Semifield Planes


We present a family of irreducible polynomials, where all the x-divisible monomials have trace zero, and use them to show that there are semifields of order 2r, for any odd integer r in [5, 31] except 21 and 27, containing GF(4). Hence these semifields are fractional dimensional.

DOI Code: 10.1285/i15900932v32n2p57

Keywords: Knuth Semifields; fractional dimension

Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.