MinT - Information on Result #1819126

Information on Result #1819126

OA(32⁸⁰, 292, S₃₂, 46), using discarding parts of the base based on linear OA(128⁵⁷, 292, F₁₂₈, 46) (dual of [292, 235, 47]-code), using

constructionÂ X applied to AG(F,240P) âŠ‚ AG(F,243P) [i] based on
1. linear OA(128⁵⁵, 287, F₁₂₈, 46) (dual of [287, 232, 47]-code), using algebraic-geometric code AG(F,240P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
  - a function field by SÃ©mirat [i]
2. linear OA(128⁵², 287, F₁₂₈, 43) (dual of [287, 235, 44]-code), using algebraic-geometric code AG(F,243P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (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(32⁸¹, 293, S₃₂, 46)	[i]		Code Embedding in Larger Space
2	OA(32⁸², 294, S₃₂, 46)	[i]		Code Embedding in Larger Space