MinT - Information on Result #2163832

Information on Result #2163832

There is no linear OA(4⁷⁵, 80, F₄, 58) (dual of [80, 5, 59]-code), because 2 times truncation would yield linear OA(4⁷³, 78, F₄, 56) (dual of [78, 5, 57]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4⁷², 75, F₄, 56) (dual of [75, 3, 57]-code), but
  - Griesmer bound [i]
2. linear OA(4⁵, 78, F₄, 3) (dual of [78, 73, 4]-code or 78-cap in PG(4,4)), but
  - discarding factors / shortening the dual code would yield linear OA(4⁵, 42, F₄, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
    - 41 is the largest size of a cap in PG(4,Â 4) [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.