MinT - Information on Result #815669

Information on Result #815669

Linear OOA(3⁵⁵, 30, F₃, 2, 36) (dual of [(30, 2), 5, 37]-NRT-code), using OOA 2-folding based on linear OA(3⁵⁵, 60, F₃, 36) (dual of [60, 5, 37]-code), using

juxtaposition [i] based on
1. linear OA(3⁰, 5, F₃, 0) (dual of [5, 5, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]
2. linear OA(3⁵⁰, 55, F₃, 35) (dual of [55, 5, 36]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
      2. nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
        20 is the largest size of a cap in PG(4,Â 3) [i]

Mode: Constructive and 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.