MinT - Information on Result #1817168

Information on Result #1817168

OA(32⁸⁴, 181, S₃₂, 61), using discarding parts of the base based on linear OA(64⁷⁰, 181, F₆₄, 61) (dual of [181, 111, 62]-code), using

constructionÂ X applied to AG(F,114P) âŠ‚ AG(F,117P) [i] based on
1. linear OA(64⁶⁸, 176, F₆₄, 61) (dual of [176, 108, 62]-code), using algebraic-geometric code AG(F,114P) [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(64⁶⁵, 176, F₆₄, 58) (dual of [176, 111, 59]-code), using algebraic-geometric code AG(F,117P) [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(32⁸⁵, 182, S₃₂, 61)	[i]		Code Embedding in Larger Space
2	OA(32⁸⁶, 183, S₃₂, 61)	[i]		Code Embedding in Larger Space