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The non-existence of $(104,22;3,5)$-arcs

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  • Using some recent results about multiple extendability of arcs and codes, we prove the nonexistence of $(104,22)$-arcs in $PG(3,5)$. This implies the non-existence of Griesmer $[104,4,82]_5$-codes and settles one of the four remaining open cases for the main problem of coding theory for $q=5,k=4,d=82$.
    Mathematics Subject Classification: Primary: 51C05, 51E21, 51E22; Secondary: 94B05.


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