MinT - Information on Result #576633

Information on Result #576633

There is no linear OOA(7¹⁰, 42, F₇, 3, 8) (dual of [(42, 3), 116, 9]-NRT-code), because 2 times depth reduction would yield linear OA(7¹⁰, 42, F₇, 8) (dual of [42, 32, 9]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(7⁹, 14, F₇, 8) (dual of [14, 5, 9]-code), but
  - â€œMPaâ€ bound on codes from Brouwerâ€™s database [i]
2. 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.