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On codes over FFN$(1,q)$-projective varieties

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  • For projective varieties defined over a finite field ${\mathbb F}_q$ we show that they contain a unique subvariety that satisfies the Finite Field Nullstellensatz property [1,2], for homogeneous linear polynomials over ${\mathbb F}_q$. Using these subvarieties we construct linear codes and estimate some of their parameters.
    Mathematics Subject Classification: Primary: 11T71; Secondary: 94Bxx.


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