MinT - Information on Result #1817057

Information on Result #1817057

OA(32⁷⁸, 183, S₃₂, 55), using discarding parts of the base based on linear OA(64⁶⁵, 183, F₆₄, 55) (dual of [183, 118, 56]-code), using

constructionÂ X applied to AG(F,120P) âŠ‚ AG(F,124P) [i] based on
1. linear OA(64⁶², 176, F₆₄, 55) (dual of [176, 114, 56]-code), using algebraic-geometric code AG(F,120P) [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(64⁵⁸, 176, F₆₄, 51) (dual of [176, 118, 52]-code), using algebraic-geometric code AG(F,124P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OA(64³, 7, F₆₄, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,64) or 7-cap in PG(2,64)), using
  - discarding factors / shortening the dual code based on linear OA(64³, 64, F₆₄, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
    - Reedâ€“Solomon code RS(61,64) [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(32⁷⁹, 184, S₃₂, 55)	[i]		Code Embedding in Larger Space
2	OA(32⁸⁰, 185, S₃₂, 55)	[i]		Code Embedding in Larger Space