MinT - Information on Result #1821546

Information on Result #1821546

OA(128⁷⁶, 520, S₁₂₈, 43), using discarding parts of the base based on linear OA(256⁶⁶, 520, F₂₅₆, 43) (dual of [520, 454, 44]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256²², 260, F₂₅₆, 21) (dual of [260, 238, 22]-code), using
  - constructionÂ X applied to AG(F, Q+116P) âŠ‚ AG(F, Q+117P) [i] based on
    1. linear OA(256²¹, 257, F₂₅₆, 21) (dual of [257, 236, 22]-code or 257-arc in PG(20,256)), using algebraic-geometric code AG(F, Q+116P) 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(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 (see above)
    3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(256⁴⁴, 260, F₂₅₆, 43) (dual of [260, 216, 44]-code), using
  - constructionÂ X applied to AG(F, Q+105P) âŠ‚ AG(F, Q+106P) [i] based on
    1. linear OA(256⁴³, 257, F₂₅₆, 43) (dual of [257, 214, 44]-code or 257-arc in PG(42,256)), using algebraic-geometric code AG(F, Q+105P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
    2. linear OA(256⁴¹, 257, F₂₅₆, 41) (dual of [257, 216, 42]-code or 257-arc in PG(40,256)), using algebraic-geometric code AG(F, Q+106P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
    3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code) (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.