MinT - Information on Result #559167

Information on Result #559167

There is no linear OOA(4⁵¹, 57, F₄, 2, 39) (dual of [(57, 2), 63, 40]-NRT-code), because 3 step m-reduction would yield linear OA(4⁴⁸, 57, F₄, 36) (dual of [57, 9, 37]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4⁴⁷, 51, F₄, 36) (dual of [51, 4, 37]-code), but
  - a result by Landjev, Maruta, and Hill [i]
2. OA(4⁹, 57, S₄, 6), but
  - discarding factors would yield OA(4⁹, 40, S₄, 6), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 273901 > 4⁹ [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(4⁵¹, 57, F₄, 3, 39) (dual of [(57, 3), 120, 40]-NRT-code)	[i]		Depth Reduction