MinT - Information on Result #573620

Information on Result #573620

There is no linear OOA(4¹⁶⁸, 162, F₄, 3, 130) (dual of [(162, 3), 318, 131]-NRT-code), because 1 times depth reduction would yield linear OOA(4¹⁶⁸, 162, F₄, 2, 130) (dual of [(162, 2), 156, 131]-NRT-code), but

14 step m-reduction [i] would yield linear OA(4¹⁵⁴, 162, F₄, 116) (dual of [162, 8, 117]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4¹⁵³, 158, F₄, 116) (dual of [158, 5, 117]-code), but
    - residual code [i] would yield linear OA(4³⁷, 41, F₄, 29) (dual of [41, 4, 30]-code), but
      - 1 times truncation [i] would yield linear OA(4³⁶, 40, F₄, 28) (dual of [40, 4, 29]-code), but
        residual code [i] would yield linear OA(4⁸, 11, F₄, 7) (dual of [11, 3, 8]-code), but
        improvement by Maruta on the Griesmer bound [i]
  2. OA(4⁸, 162, 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

None.