MinT - Information on Result #561153

Information on Result #561153

There is no linear OOA(4²²⁹, 215, F₄, 2, 178) (dual of [(215, 2), 201, 179]-NRT-code), because 22 step m-reduction would yield linear OA(4²⁰⁷, 215, F₄, 156) (dual of [215, 8, 157]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4²⁰⁶, 211, F₄, 156) (dual of [211, 5, 157]-code), but
  - residual code [i] would yield linear OA(4⁵⁰, 54, F₄, 39) (dual of [54, 4, 40]-code), but
    - 3 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, 215, 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]

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(4²²⁹, 215, F₄, 3, 178) (dual of [(215, 3), 416, 179]-NRT-code)	[i]		Depth Reduction