MinT - Information on Result #1821076

Information on Result #1821076

OA(128²⁸, 514, S₁₂₈, 16), using discarding parts of the base based on linear OA(256²⁴, 514, F₂₅₆, 16) (dual of [514, 490, 17]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256⁸, 257, F₂₅₆, 8) (dual of [257, 249, 9]-code or 257-arc in PG(7,256)), using
  - extended Reedâ€“Solomon code RS_e(249,256) [i]
  - algebraic-geometric code AG(F,124P) 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 = 2 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, Q+49P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
2. linear OA(256¹⁶, 257, F₂₅₆, 16) (dual of [257, 241, 17]-code or 257-arc in PG(15,256)), using
  - extended Reedâ€“Solomon code RS_e(241,256) [i]
  - algebraic-geometric code AG(F,120P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  - algebraic-geometric code AG(F,80P) 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,48P) with degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)

Mode: Constructive.

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.