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Fractional Dimensional Semifield Planes


Abstract


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

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