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A set $${\fancyscript{K}}$$ K in $$\hbox {PG}(r,4), r \ge 2$$ PG ( r , 4 ) , r ≥ 2 , is odd if every line meets $${\fancyscript{K}}$$ K in an odd number of points. We show there are exactly 45 inequivalent odd sets in $$\hbox {PG}(4,4)$$ PG ( 4 , 4 ) up to projective equivalence. As an application to coding theory, a new sufficient condition for the… (More)

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