MinT - Information on Result #1821022

Information on Result #1821022

OA(128²¹, 514, S₁₂₈, 12), using discarding parts of the base based on linear OA(256¹⁸, 514, F₂₅₆, 12) (dual of [514, 496, 13]-code), using

(u,Â u+v)-construction [i] based on
1. 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)
2. linear OA(256¹², 257, F₂₅₆, 12) (dual of [257, 245, 13]-code or 257-arc in PG(11,256)), using
  - extended Reedâ€“Solomon code RS_e(245,256) [i]
  - algebraic-geometric code AG(F,122P) 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+80P) 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, Q+48P) with degQ = 4 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.