MinT - Information on Result #1820716

Information on Result #1820716

OA(64²⁰, 262, S₆₄, 13), using discarding parts of the base based on linear OA(256¹⁵, 262, F₂₅₆, 13) (dual of [262, 247, 14]-code), using

constructionÂ X applied to AG(F,81P) âŠ‚ AG(F,82P) [i] based on
1. linear OA(256¹³, 257, F₂₅₆, 13) (dual of [257, 244, 14]-code or 257-arc in PG(12,256)), using algebraic-geometric code AG(F, Q+120P) 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(256¹⁰, 257, F₂₅₆, 10) (dual of [257, 247, 11]-code or 257-arc in PG(9,256)), using algebraic-geometric code AG(F,123P) 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(64²¹, 263, S₆₄, 13)	[i]		Code Embedding in Larger Space
2	OA(64²², 264, S₆₄, 13)	[i]		Code Embedding in Larger Space