MinT - Information on Result #2164071

Information on Result #2164071

There is no linear OA(4¹⁵⁶, 164, F₄, 118) (dual of [164, 8, 119]-code), because 2 times truncation 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.