MinT - Information on Result #560652

Information on Result #560652

There is no linear OOA(4²⁰⁹, 186, F₄, 2, 165) (dual of [(186, 2), 163, 166]-NRT-code), because 29 step m-reduction would yield linear OA(4¹⁸⁰, 186, F₄, 136) (dual of [186, 6, 137]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁷⁹, 183, F₄, 136) (dual of [183, 4, 137]-code), but
  - Griesmer bound [i]
2. linear OA(4⁶, 186, F₄, 3) (dual of [186, 180, 4]-code or 186-cap in PG(5,4)), but
  - discarding factors / shortening the dual code would yield linear OA(4⁶, 160, F₄, 3) (dual of [160, 154, 4]-code or 160-cap in PG(5,4)), but
    - 1 times Hill recurrence [i] would yield linear OA(4⁵, 42, F₄, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
      - 41 is the largest size of a cap in PG(4,Â 4) [i]

Mode: Bound (linear).

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	No linear OOA(4²⁰⁹, 186, F₄, 3, 165) (dual of [(186, 3), 349, 166]-NRT-code)	[i]		Depth Reduction