MinT - Information on Result #2190302

Information on Result #2190302

Linear OA(3⁶¹, 67, F₃, 39) (dual of [67, 6, 40]-code), using strength reduction based on linear OA(3⁶¹, 67, F₃, 40) (dual of [67, 6, 41]-code), using

juxtaposition [i] based on
1. linear OA(3⁵, 11, F₃, 4) (dual of [11, 6, 5]-code), using
  - Golay code G(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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.