MinT - Information on Result #2295281

Information on Result #2295281

OA(128²⁵, 263, S₁₂₈, 19), using 1 times code embedding in larger space based on OA(128²⁴, 262, S₁₂₈, 19), using

discarding parts of the base [i] based on linear OA(256²¹, 262, F₂₅₆, 19) (dual of [262, 241, 20]-code), using
- constructionÂ X applied to AG(F,79P) âŠ‚ AG(F,80P) [i] based on
  1. linear OA(256¹⁹, 257, F₂₅₆, 19) (dual of [257, 238, 20]-code or 257-arc in PG(18,256)), using algebraic-geometric code AG(F, Q+117P) with degQ = 3 and 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]
  2. linear OA(256¹⁶, 257, F₂₅₆, 16) (dual of [257, 241, 17]-code or 257-arc in PG(15,256)), using 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)
  3. linear OA(256², 5, F₂₅₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
    - discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
      - Reedâ€“Solomon code RS(254,256) [i]

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.