MinT - Information on Result #1845208

Information on Result #1845208

OA(27⁸⁴, 302, S₂₇, 49), using discarding parts of the base based on linear OA(81⁶³, 302, F₈₁, 49) (dual of [302, 239, 50]-code), using

constructionÂ X applied to AG(F,247P) âŠ‚ AG(F,250P) [i] based on
1. linear OA(81⁶¹, 297, F₈₁, 49) (dual of [297, 236, 50]-code), using algebraic-geometric code AG(F,247P) [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
  - a curve from the manYPoints database [i]
2. linear OA(81⁵⁸, 297, F₈₁, 46) (dual of [297, 239, 47]-code), using algebraic-geometric code AG(F,250P) [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298 (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: Arbitrary.

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(27⁸⁵, 303, S₂₇, 49)	[i]		Code Embedding in Larger Space
2	OA(27⁸⁶, 304, S₂₇, 49)	[i]		Code Embedding in Larger Space