MinT - Information on Result #587495

Information on Result #587495

There is no linear OOA(3²³, 37, F₃, 5, 15) (dual of [(37, 5), 162, 16]-NRT-code), because 4 times depth reduction would yield linear OA(3²³, 37, F₃, 15) (dual of [37, 14, 16]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3²², 28, F₃, 15) (dual of [28, 6, 16]-code), but
  - â€œHHMâ€ bound on codes from Brouwerâ€™s database [i]
2. linear OA(3¹⁴, 37, F₃, 9) (dual of [37, 23, 10]-code), but
  - discarding factors / shortening the dual code would yield linear OA(3¹⁴, 31, F₃, 9) (dual of [31, 17, 10]-code), but
    - residual code [i] would yield linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), but
      - 20 is the largest size of a cap in PG(4,Â 3) [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.