MinT - Information on Result #815564

Information on Result #815564

Linear OOA(3⁸³, 59, F₃, 2, 35) (dual of [(59, 2), 35, 36]-NRT-code), using OOA 2-folding based on linear OA(3⁸³, 118, F₃, 35) (dual of [118, 35, 36]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(3³⁰, 59, F₃, 17) (dual of [59, 29, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(3³⁰, 60, F₃, 17) (dual of [60, 30, 18]-code), using
    - extended quadratic residue code Q_e(60,3) [i]
2. linear OA(3⁵³, 59, F₃, 35) (dual of [59, 6, 36]-code), using
  - 3 times code embedding in larger space [i] 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.