MinT - Information on Result #1303609

Information on Result #1303609

Linear OA(16¹³, 516, F₁₆, 6) (dual of [516, 503, 7]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(16¹², 514, F₁₆, 6) (dual of [514, 502, 7]-code), using
- trace code [i] based on linear OA(256⁶, 257, F₂₅₆, 6) (dual of [257, 251, 7]-code or 257-arc in PG(5,256)), using
  - extended Reedâ€“Solomon code RS_e(251,256) [i]
  - algebraic-geometric code AG(F,125P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
  - algebraic-geometric code AG(F, Q+82P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  - algebraic-geometric code AG(F,50P) with degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
linear OA(16¹², 515, F₁₆, 5) (dual of [515, 503, 6]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 16¹²Â > V_b^sâˆ’1(kâˆ’1)Â = 145 596792 247936 [i]
linear OA(16⁰, 1, F₁₆, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(16¹³, 516, F₁₆, 2, 6) (dual of [(516, 2), 1019, 7]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (7, 13, 516)-net over F₁₆	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound