MinT - Information on Result #1050654

Information on Result #1050654

Linear OOA(3¹⁷, 230, F₃, 4, 5) (dual of [(230, 4), 903, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(3¹⁷, 231, F₃, 2, 5) (dual of [(231, 2), 445, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3¹, 77, F₃, 2, 1) (dual of [(77, 2), 153, 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, 77, F₃, 2, 2) (dual of [(77, 2), 149, 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(3¹¹, 77, F₃, 2, 5) (dual of [(77, 2), 143, 6]-NRT-code), using
  - extracting embedded OOA [i] based on digital (6, 11, 77)-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		Method
1	Linear OOA(3¹⁰⁸, 2097380, F₃, 4, 10) (dual of [(2097380, 4), 8389412, 11]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁴⁷, 4194531, F₃, 4, 10) (dual of [(4194531, 4), 16777977, 11]-NRT-code)	[i]
3	Linear OOA(3¹²³, 2097380, F₃, 4, 11) (dual of [(2097380, 4), 8389397, 12]-NRT-code)	[i]
4	Linear OOA(3¹⁴⁵, 2391718, F₃, 4, 11) (dual of [(2391718, 4), 9566727, 12]-NRT-code)	[i]
5	Linear OOA(3¹⁶³, 4194531, F₃, 4, 11) (dual of [(4194531, 4), 16777961, 12]-NRT-code)	[i]