MinT - Information on Result #955203

Information on Result #955203

Linear OOA(3⁶³, 23, F₃, 3, 41) (dual of [(23, 3), 6, 42]-NRT-code), using OOA 3-folding based on linear OA(3⁶³, 69, F₃, 41) (dual of [69, 6, 42]-code), using

1 times code embedding in larger space [i] based on linear OA(3⁶², 68, F₃, 41) (dual of [68, 6, 42]-code), using
- juxtaposition [i] based on
  1. linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
    - extended Golay code G_e(3) [i]
  2. 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.