MinT - Information on Result #815423

Information on Result #815423

Linear OOA(3⁴⁹, 27, F₃, 2, 34) (dual of [(27, 2), 5, 35]-NRT-code), using OOA 2-folding based on linear OA(3⁴⁹, 54, F₃, 34) (dual of [54, 5, 35]-code), using

discarding factors / shortening the dual code based on linear OA(3⁴⁹, 55, F₃, 34) (dual of [55, 6, 35]-code), using
- 1 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.

Other Results with Identical Parameters

Algebraic-Geometric NRT-Codes [i]

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁴⁰, 81, F₃, 2, 68) (dual of [(81, 2), 22, 69]-NRT-code)	[i]		Generalized (u,Â u+v)-Construction for OOAs