MinT - Information on Result #1817416

Information on Result #1817416

OA(32⁹⁶, 185, S₃₂, 69), using discarding parts of the base based on linear OA(64⁸⁰, 185, F₆₄, 69) (dual of [185, 105, 70]-code), using

constructionÂ X applied to AG(F,106P) âŠ‚ AG(F,111P) [i] based on
1. linear OA(64⁷⁶, 176, F₆₄, 69) (dual of [176, 100, 70]-code), using algebraic-geometric code AG(F,106P) [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(64⁷¹, 176, F₆₄, 64) (dual of [176, 105, 65]-code), using algebraic-geometric code AG(F,111P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OA(64⁴, 9, F₆₄, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,64)), using
  - discarding factors / shortening the dual code based on linear OA(64⁴, 64, F₆₄, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
    - Reedâ€“Solomon code RS(60,64) [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, 186, S₃₂, 69)	[i]		Code Embedding in Larger Space
2	OA(32⁹⁸, 187, S₃₂, 69)	[i]		Code Embedding in Larger Space