MinT - Information on Result #576712

Information on Result #576712

There is no linear OOA(7⁴³, 45, F₇, 3, 38) (dual of [(45, 3), 92, 39]-NRT-code), because 1 times depth reduction would yield linear OOA(7⁴³, 45, F₇, 2, 38) (dual of [(45, 2), 47, 39]-NRT-code), but

8 step m-reduction [i] would yield linear OA(7³⁵, 45, F₇, 30) (dual of [45, 10, 31]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(7³⁴, 37, F₇, 30) (dual of [37, 3, 31]-code), but
    - â€œHi4â€ bound on codes from Brouwerâ€™s database [i]
  2. linear OA(7¹⁰, 45, F₇, 8) (dual of [45, 35, 9]-code), but
    - discarding factors / shortening the dual code would yield linear OA(7¹⁰, 42, F₇, 8) (dual of [42, 32, 9]-code), but
      - constructionÂ Y1 [i] would yield
        linear OA(7⁹, 14, F₇, 8) (dual of [14, 5, 9]-code), but
        â€œMPaâ€ bound on codes from Brouwerâ€™s database [i]
        linear OA(7³², 42, F₇, 28) (dual of [42, 10, 29]-code), but
        discarding factors / shortening the dual code would yield linear OA(7³², 38, F₇, 28) (dual of [38, 6, 29]-code), but
        residual code [i] would yield linear OA(7⁴, 9, F₇, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,7)), but
        bound for MDS codes [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.