Abstract
A finite semifield D is considered a fractional dimensional semifield if it contains a subsemifield E such that λ := log|E||D| is not an integer. We develop spread-theoretic tools to determine when finite planes admit coordinatization by fractional semifields, and to find such semifields when they exist. We use our results to show that such semifields exist for prime powers 3n whenever n is an odd integer divisible by 5 or 7.
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Communicated by S. Ball.
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Cordero, M., Jha, V. Fractional dimensions in semifields of odd order. Des. Codes Cryptogr. 61, 197–221 (2011). https://doi.org/10.1007/s10623-010-9448-y
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DOI: https://doi.org/10.1007/s10623-010-9448-y