MinT - Information on Result #560360

Information on Result #560360

There is no linear OOA(4¹⁹⁵, 208, F₄, 2, 146) (dual of [(208, 2), 221, 147]-NRT-code), because 2 step m-reduction would yield linear OA(4¹⁹³, 208, F₄, 144) (dual of [208, 15, 145]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁹², 200, F₄, 144) (dual of [200, 8, 145]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(4¹⁹¹, 196, F₄, 144) (dual of [196, 5, 145]-code), but
      - residual code [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, 200, 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, 208, 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(4¹⁹⁵, 208, F₄, 3, 146) (dual of [(208, 3), 429, 147]-NRT-code)	[i]		Depth Reduction