MinT - Information on Result #1820554

Information on Result #1820554

OA(32⁵⁶, 262, S₃₂, 33), using discarding parts of the base based on linear OA(256³⁵, 262, F₂₅₆, 33) (dual of [262, 227, 34]-code), using

constructionÂ X applied to AG(F, Q+73P) âŠ‚ AG(F, Q+74P) [i] based on
1. linear OA(256³³, 257, F₂₅₆, 33) (dual of [257, 224, 34]-code or 257-arc in PG(32,256)), using algebraic-geometric code AG(F, Q+110P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
2. linear OA(256³⁰, 257, F₂₅₆, 30) (dual of [257, 227, 31]-code or 257-arc in PG(29,256)), using algebraic-geometric code AG(F,113P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
3. linear OA(256², 5, F₂₅₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
  - discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
    - Reedâ€“Solomon code RS(254,256) [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(32⁵⁷, 263, S₃₂, 33)	[i]		Code Embedding in Larger Space
2	OA(32⁵⁸, 264, S₃₂, 33)	[i]		Code Embedding in Larger Space