MinT - Information on Result #560433

Information on Result #560433

There is no linear OOA(4¹⁹⁹, 213, F₄, 2, 149) (dual of [(213, 2), 227, 150]-NRT-code), because 1 step m-reduction would yield linear OA(4¹⁹⁸, 213, F₄, 148) (dual of [213, 15, 149]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁹⁷, 205, F₄, 148) (dual of [205, 8, 149]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(4¹⁹⁶, 201, F₄, 148) (dual of [201, 5, 149]-code), but
      - residual code [i] would yield linear OA(4⁴⁸, 52, F₄, 37) (dual of [52, 4, 38]-code), but
        1 times truncation [i] would yield linear OA(4⁴⁷, 51, F₄, 36) (dual of [51, 4, 37]-code), but
        a result by Landjev, Maruta, and Hill [i]
    2. OA(4⁸, 205, S₄, 4), but
      - discarding factors would yield OA(4⁸, 121, S₄, 4), but
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 65704 > 4⁸ [i]
2. OA(4¹⁵, 213, S₄, 8), but
  - discarding factors would yield OA(4¹⁵, 135, S₄, 8), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 1082 768311 > 4¹⁵ [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(4¹⁹⁹, 213, F₄, 3, 149) (dual of [(213, 3), 440, 150]-NRT-code)	[i]		Depth Reduction