MinT - Information on Result #1820140

Information on Result #1820140

OA(64⁷⁴, 294, S₆₄, 51), using discarding parts of the base based on linear OA(128⁶³, 294, F₁₂₈, 51) (dual of [294, 231, 52]-code), using

constructionÂ X applied to AG(F,235P) âŠ‚ AG(F,239P) [i] based on
1. linear OA(128⁶⁰, 287, F₁₂₈, 51) (dual of [287, 227, 52]-code), using algebraic-geometric code AG(F,235P) [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(128⁵⁶, 287, F₁₂₈, 47) (dual of [287, 231, 48]-code), using algebraic-geometric code AG(F,239P) [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(8¹⁴⁸, 588, S₈, 51)	[i]		Trace Code