MinT - Information on Result #546577

Information on Result #546577

There is no linear OA(3³¹, 44, F₃, 21) (dual of [44, 13, 22]-code), because residual code would yield linear OA(3¹⁰, 22, F₃, 7) (dual of [22, 12, 8]-code), but

discarding factors / shortening the dual code would yield linear OA(3¹⁰, 21, F₃, 7) (dual of [21, 11, 8]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3⁹, 13, F₃, 7) (dual of [13, 4, 8]-code), but
    - 1 times truncation [i] would yield linear OA(3⁸, 12, F₃, 6) (dual of [12, 4, 7]-code), but
      - residual code [i] would yield linear OA(3², 5, F₃, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,3)), but
        improvement by Maruta on the Griesmer bound [i]
  2. OA(3¹¹, 21, S₃, 8), but
    - the linear programming bound shows that MÂ â‰¥ 3018 053439 / 15926 > 3¹¹ [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.