MinT - Information on Result #1821189

Information on Result #1821189

OA(128⁴⁰, 520, S₁₂₈, 22), using discarding parts of the base based on linear OA(256³⁵, 520, F₂₅₆, 22) (dual of [520, 485, 23]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256¹², 260, F₂₅₆, 11) (dual of [260, 248, 12]-code), using
  - constructionÂ X applied to AG(F, Q+121P) âŠ‚ AG(F, Q+122P) [i] based on
    1. linear OA(256¹¹, 257, F₂₅₆, 11) (dual of [257, 246, 12]-code or 257-arc in PG(10,256)), using algebraic-geometric code AG(F, Q+121P) 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(256⁹, 257, F₂₅₆, 9) (dual of [257, 248, 10]-code or 257-arc in PG(8,256)), using algebraic-geometric code AG(F, Q+122P) 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(256²³, 260, F₂₅₆, 22) (dual of [260, 237, 23]-code), using
  - constructionÂ X applied to AG(F,117P) âŠ‚ AG(F,118P) [i] based on
    1. linear OA(256²², 257, F₂₅₆, 22) (dual of [257, 235, 23]-code or 257-arc in PG(21,256)), using 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 (see above)
    2. linear OA(256²⁰, 257, F₂₅₆, 20) (dual of [257, 237, 21]-code or 257-arc in PG(19,256)), using algebraic-geometric code AG(F,118P) with 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

The following results depend on this result:

	Result		This result only	Method
1	OA(128⁴¹, 521, S₁₂₈, 22)	[i]		Code Embedding in Larger Space