MinT - Information on Result #590353

Information on Result #590353

There is no linear OOA(3²¹⁶, 154, F₃, 5, 168) (dual of [(154, 5), 554, 169]-NRT-code), because 3 times depth reduction would yield linear OOA(3²¹⁶, 154, F₃, 2, 168) (dual of [(154, 2), 92, 169]-NRT-code), but

69 step m-reduction [i] would yield linear OA(3¹⁴⁷, 154, F₃, 99) (dual of [154, 7, 100]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁴⁶, 151, F₃, 99) (dual of [151, 5, 100]-code), but
    - Griesmer bound [i]
  2. linear OA(3⁷, 154, F₃, 3) (dual of [154, 147, 4]-code or 154-cap in PG(6,3)), but
    - discarding factors / shortening the dual code would yield linear OA(3⁷, 137, F₃, 3) (dual of [137, 130, 4]-code or 137-cap in PG(6,3)), but
      - a result by BarÃ¡t, Edel, Hill, and Storme [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.