MinT - Information on Result #1819247

Information on Result #1819247

OA(32⁹⁴, 296, S₃₂, 54), using discarding parts of the base based on linear OA(128⁶⁷, 296, F₁₂₈, 54) (dual of [296, 229, 55]-code), using

constructionÂ X applied to AG(F,232P) âŠ‚ AG(F,237P) [i] based on
1. linear OA(128⁶³, 287, F₁₂₈, 54) (dual of [287, 224, 55]-code), using algebraic-geometric code AG(F,232P) [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(128⁵⁸, 287, F₁₂₈, 49) (dual of [287, 229, 50]-code), using algebraic-geometric code AG(F,237P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288 (see above)
3. linear OA(128⁴, 9, F₁₂₈, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,128)), using
  - discarding factors / shortening the dual code based on linear OA(128⁴, 128, F₁₂₈, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
    - Reedâ€“Solomon code RS(124,128) [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(32⁹⁵, 297, S₃₂, 54)	[i]		Code Embedding in Larger Space
2	OA(32⁹⁶, 298, S₃₂, 54)	[i]		Code Embedding in Larger Space