MinT - Information on Result #1817418

Information on Result #1817418

OA(32⁹⁶, 181, S₃₂, 71), using discarding parts of the base based on linear OA(64⁸⁰, 181, F₆₄, 71) (dual of [181, 101, 72]-code), using

constructionÂ X applied to AG(F,104P) âŠ‚ AG(F,107P) [i] based on
1. linear OA(64⁷⁸, 176, F₆₄, 71) (dual of [176, 98, 72]-code), using algebraic-geometric code AG(F,104P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]
2. linear OA(64⁷⁵, 176, F₆₄, 68) (dual of [176, 101, 69]-code), using algebraic-geometric code AG(F,107P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OA(64², 5, F₆₄, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,64)), using
  - discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
    - Reedâ€“Solomon code RS(62,64) [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(32⁹⁷, 182, S₃₂, 71)	[i]		Code Embedding in Larger Space
2	OA(32⁹⁸, 183, S₃₂, 71)	[i]		Code Embedding in Larger Space