MinT - Information on Result #572808

Information on Result #572808

There is no linear OOA(4⁶⁸, 68, F₄, 3, 53) (dual of [(68, 3), 136, 54]-NRT-code), because 1 times depth reduction would yield linear OOA(4⁶⁸, 68, F₄, 2, 53) (dual of [(68, 2), 68, 54]-NRT-code), but

5 step m-reduction [i] would yield linear OA(4⁶³, 68, F₄, 48) (dual of [68, 5, 49]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4⁶², 65, F₄, 48) (dual of [65, 3, 49]-code), but
    - Griesmer bound [i]
  2. linear OA(4⁵, 68, F₄, 3) (dual of [68, 63, 4]-code or 68-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.

Other Results with Identical Parameters

None.

Depending Results

None.