MinT - Information on Result #1818196

Information on Result #1818196

OA(27⁸⁰, 178, S₂₇, 50), using discarding parts of the base based on linear OA(81⁶⁰, 178, F₈₁, 50) (dual of [178, 118, 51]-code), using

constructionÂ X applied to AG(F,120P) âŠ‚ AG(F,124P) [i] based on
1. linear OA(81⁵⁷, 171, F₈₁, 50) (dual of [171, 114, 51]-code), using algebraic-geometric code AG(F,120P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
  - a function field by SÃ©mirat [i]
2. linear OA(81⁵³, 171, F₈₁, 46) (dual of [171, 118, 47]-code), using algebraic-geometric code AG(F,124P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172 (see above)
3. linear OA(81³, 7, F₈₁, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,81) or 7-cap in PG(2,81)), using
  - discarding factors / shortening the dual code based on linear OA(81³, 81, F₈₁, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
    - Reedâ€“Solomon code RS(78,81) [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(27⁸¹, 179, S₂₇, 50)	[i]		Code Embedding in Larger Space
2	OA(27⁸², 180, S₂₇, 50)	[i]		Code Embedding in Larger Space