MinT - Information on Result #560653

Information on Result #560653

There is no linear OOA(4²⁰⁹, 181, F₄, 2, 166) (dual of [(181, 2), 153, 167]-NRT-code), because 34 step m-reduction would yield linear OA(4¹⁷⁵, 181, F₄, 132) (dual of [181, 6, 133]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁷⁴, 178, F₄, 132) (dual of [178, 4, 133]-code), but
  - Griesmer bound [i]
2. linear OA(4⁶, 181, F₄, 3) (dual of [181, 175, 4]-code or 181-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, 181, F₄, 3, 166) (dual of [(181, 3), 334, 167]-NRT-code)	[i]		Depth Reduction