MinT - Information on Result #1818031

Information on Result #1818031

OA(27⁶⁴, 176, S₂₇, 39), using discarding parts of the base based on linear OA(81⁴⁸, 176, F₈₁, 39) (dual of [176, 128, 40]-code), using

constructionÂ X applied to AG(F,131P) âŠ‚ AG(F,134P) [i] based on
1. linear OA(81⁴⁶, 171, F₈₁, 39) (dual of [171, 125, 40]-code), using algebraic-geometric code AG(F,131P) [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(81⁴³, 171, F₈₁, 36) (dual of [171, 128, 37]-code), using algebraic-geometric code AG(F,134P) [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172 (see above)
3. linear OA(81², 5, F₈₁, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,81)), using
  - discarding factors / shortening the dual code based on linear OA(81², 81, F₈₁, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
    - Reedâ€“Solomon code RS(79,81) [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(27⁶⁵, 177, S₂₇, 39)	[i]		Code Embedding in Larger Space
2	OA(27⁶⁶, 178, S₂₇, 39)	[i]		Code Embedding in Larger Space