The non-existence of [29+h, 3+h, 26]16 and [29+h, 4+h, 25]16-codes, h ≥ 0, is proven. These results are obtained using geometrical methods, exploiting the equivalence betweenNMDScodes of dimension 3 and (n, 3)-arcs in PG(2, q). Along theway the packing problem for complete (n, 3)-arcs in PG(2, 16) is solved, proving that m3(2, 16) = 28 and t3(2, 16) = 15 and that the complete (28, 3)-arc and the complete (15, 3)-arc are unique up to collineations.
The non-existence of some NMDS codes and the extremal sizes of complete (n, 3)-arcs in PG(2, 16)
BARTOLI, DANIELE;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2014
Abstract
The non-existence of [29+h, 3+h, 26]16 and [29+h, 4+h, 25]16-codes, h ≥ 0, is proven. These results are obtained using geometrical methods, exploiting the equivalence betweenNMDScodes of dimension 3 and (n, 3)-arcs in PG(2, q). Along theway the packing problem for complete (n, 3)-arcs in PG(2, 16) is solved, proving that m3(2, 16) = 28 and t3(2, 16) = 15 and that the complete (28, 3)-arc and the complete (15, 3)-arc are unique up to collineations.File in questo prodotto:
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