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Maximal three-independent subsets of {0, 1, 2}n

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Abstract

We consider a variant of the classical problem of finding the size of the largest cap in ther-dimensional projective geometry PG(r, 3) over the field IF3 with 3 elements. We study the maximum sizef(n) of a subsetS of IF n3 with the property that the only solution to the equationx 1+x2+x3=0 isx 1=x2=x3. Letc n=f(n)1/n andc=sup{c 1, c2, ...}. We prove thatc>2.21, improving the previous lower bound of 2.1955 ...

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  1. Mathematical Sciences Research Center, AT&T Bell Laboratories, 07974, Murray Hill, NJ

    A. R. Calderbank & P. C. Fishburn

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  1. A. R. Calderbank
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  2. P. C. Fishburn
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Communicated by S. Vanstone

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Calderbank, A.R., Fishburn, P.C. Maximal three-independent subsets of {0, 1, 2}n . Des Codes Crypt 4, 203–211 (1994). https://doi.org/10.1007/BF01388452

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