MinT - Information on Result #1820082

Information on Result #1820082

OA(64⁷⁰, 298, S₆₄, 46), using discarding parts of the base based on linear OA(128⁶⁰, 298, F₁₂₈, 46) (dual of [298, 238, 47]-code), using

constructionÂ X applied to AG(F,240P) âŠ‚ AG(F,246P) [i] based on
1. linear OA(128⁵⁵, 287, F₁₂₈, 46) (dual of [287, 232, 47]-code), using algebraic-geometric code AG(F,240P) [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(128⁴⁹, 287, F₁₂₈, 40) (dual of [287, 238, 41]-code), using algebraic-geometric code AG(F,246P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
3. linear OA(128⁵, 11, F₁₂₈, 5) (dual of [11, 6, 6]-code or 11-arc in PG(4,128)), using
  - discarding factors / shortening the dual code based on linear OA(128⁵, 128, F₁₂₈, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
    - Reedâ€“Solomon code RS(123,128) [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(64⁷¹, 299, S₆₄, 46)	[i]		Code Embedding in Larger Space
2	OA(64⁷², 300, S₆₄, 46)	[i]		Code Embedding in Larger Space
3	OA(8¹⁴⁰, 596, S₈, 46)	[i]		Trace Code