MinT - Information on Result #576423

Information on Result #576423

There is no linear OOA(5⁹⁹, 68, F₅, 3, 87) (dual of [(68, 3), 105, 88]-NRT-code), because 1 times depth reduction would yield linear OOA(5⁹⁹, 68, F₅, 2, 87) (dual of [(68, 2), 37, 88]-NRT-code), but

37 step m-reduction [i] would yield linear OA(5⁶², 68, F₅, 50) (dual of [68, 6, 51]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(5⁶¹, 64, F₅, 50) (dual of [64, 3, 51]-code), but
    - Griesmer bound [i]
  2. OA(5⁶, 68, S₅, 4), but
    - discarding factors would yield OA(5⁶, 45, S₅, 4), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 16021 > 5⁶ [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.