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A Note on a Specific Pencil of Conics in the Galois Fields of Order 2^n

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Preprint
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arXiv ID: math/0012214
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arXiv
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Abstract

The pencil of conics featuring three degenerate conics each of which is a line-pair is briefly inspected in a Galois field of characteristic two. It is shown that if two degenerates are conjugate imaginary line pairs, the third must be a real line pair; this contradicts Campbell's claim (Campbell 1927) that all the three singular conics are conjugate imaginary line pairs.

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