MinT - Information on Result #547886

Information on Result #547886

There is no linear OA(4¹⁶⁰, 175, F₄, 120) (dual of [175, 15, 121]-code), because constructionÂ Y1 would yield

linear OA(4¹⁵⁹, 167, F₄, 120) (dual of [167, 8, 121]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4¹⁵⁸, 163, F₄, 120) (dual of [163, 5, 121]-code), but
    - residual code [i] would yield linear OA(4³⁸, 42, F₄, 30) (dual of [42, 4, 31]-code), but
      - 2 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, 167, 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]
OA(4¹⁵, 175, 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).

None.

None.