MinT - Information on Result #1819367

Information on Result #1819367

OA(32¹⁰⁸, 294, S₃₂, 65), using discarding parts of the base based on linear OA(128⁷⁷, 294, F₁₂₈, 65) (dual of [294, 217, 66]-code), using

constructionÂ X applied to AG(F,221P) âŠ‚ AG(F,225P) [i] based on
1. linear OA(128⁷⁴, 287, F₁₂₈, 65) (dual of [287, 213, 66]-code), using algebraic-geometric code AG(F,221P) [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(128⁷⁰, 287, F₁₂₈, 61) (dual of [287, 217, 62]-code), using algebraic-geometric code AG(F,225P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
3. linear OA(128³, 7, F₁₂₈, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,128) or 7-cap in PG(2,128)), using
  - discarding factors / shortening the dual code based on linear OA(128³, 128, F₁₂₈, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
    - Reedâ€“Solomon code RS(125,128) [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, 295, S₃₂, 65)	[i]		Code Embedding in Larger Space
2	OA(32¹¹⁰, 296, S₃₂, 65)	[i]		Code Embedding in Larger Space