MinT - Information on Result #2266406

Information on Result #2266406

Linear OA(3⁵¹, 57, F₃, 33) (dual of [57, 6, 34]-code), using 3 times code embedding in larger space based on linear OA(3⁴⁸, 54, F₃, 33) (dual of [54, 6, 34]-code), using

2 times truncation [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.

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

Other Results with Identical Parameters

None.

Depending Results

None.