MinT - Information on Result #1845816

Information on Result #1845816

OA(128¹⁶, 546, S₁₂₈, 9), using discarding parts of the base based on linear OA(256¹⁴, 546, F₂₅₆, 9) (dual of [546, 532, 10]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256⁴, 257, F₂₅₆, 4) (dual of [257, 253, 5]-code or 257-arc in PG(3,256)), using
  - extended Reedâ€“Solomon code RS_e(253,256) [i]
  - algebraic-geometric code AG(F,126P) 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,84P) with 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, Q+50P) with degQ = 2 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
2. linear OA(256¹⁰, 289, F₂₅₆, 9) (dual of [289, 279, 10]-code), using
  - extended algebraic-geometric code AG_e(F,279P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

Mode: Arbitrary.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.