MinT - Information on Result #1821547

Information on Result #1821547

OA(128⁷⁶, 514, S₁₂₈, 44), using discarding parts of the base based on linear OA(256⁶⁶, 514, F₂₅₆, 44) (dual of [514, 448, 45]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256²², 257, F₂₅₆, 22) (dual of [257, 235, 23]-code or 257-arc in PG(21,256)), using
  - extended Reedâ€“Solomon code RS_e(235,256) [i]
  - algebraic-geometric code AG(F,117P) 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,78P) 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+46P) with degQ = 4 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
2. linear OA(256⁴⁴, 257, F₂₅₆, 44) (dual of [257, 213, 45]-code or 257-arc in PG(43,256)), using
  - extended Reedâ€“Solomon code RS_e(213,256) [i]
  - algebraic-geometric code AG(F,106P) 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, Q+70P) 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+42P) with degQ = 2 and 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.