MinT - Information on Result #1819372

Information on Result #1819372

OA(32¹⁰⁸, 220, S₃₂, 70), using discarding parts of the base based on linear OA(128⁷⁷, 220, F₁₂₈, 70) (dual of [220, 143, 71]-code), using

constructionÂ X applied to AG(F,144P) âŠ‚ AG(F,147P) [i] based on
1. linear OA(128⁷⁵, 215, F₁₂₈, 70) (dual of [215, 140, 71]-code), using algebraic-geometric code AG(F,144P) [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
  - a function field by SÃ©mirat [i]
2. linear OA(128⁷², 215, F₁₂₈, 67) (dual of [215, 143, 68]-code), using algebraic-geometric code AG(F,147P) [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216 (see above)
3. linear OA(128², 5, F₁₂₈, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,128)), using
  - discarding factors / shortening the dual code based on linear OA(128², 128, F₁₂₈, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
    - Reedâ€“Solomon code RS(126,128) [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

The following results depend on this result:

	Result		This result only	Method
1	OA(32¹⁰⁹, 221, S₃₂, 70)	[i]		Code Embedding in Larger Space
2	OA(32¹¹⁰, 222, S₃₂, 70)	[i]		Code Embedding in Larger Space