MinT - Information on Result #944389

Information on Result #944389

Linear OOA(3¹⁸, 284, F₃, 3, 5) (dual of [(284, 3), 834, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(3¹⁸, 285, F₃, 2, 5) (dual of [(285, 2), 552, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3¹, 95, F₃, 2, 1) (dual of [(95, 2), 189, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
2. linear OOA(3⁵, 95, F₃, 2, 2) (dual of [(95, 2), 185, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁵, 121, F₃, 2, 2) (dual of [(121, 2), 237, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(3⁵, 121, F₃, 2) (dual of [121, 116, 3]-code), using
      - Hamming code H(5,3) [i]
3. linear OOA(3¹², 95, F₃, 2, 5) (dual of [(95, 2), 178, 6]-NRT-code), using
  - extracting embedded OOA [i] based on digital (7, 12, 95)-net over F₃, using
    - linear code embedding found in a computer search [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁰⁹, 2796485, F₃, 3, 10) (dual of [(2796485, 3), 8389346, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹²⁴, 2796485, F₃, 3, 11) (dual of [(2796485, 3), 8389331, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs