MinT - Information on Result #1050850

Information on Result #1050850

Linear OOA(81¹², 12961, F₈₁, 4, 5) (dual of [(12961, 4), 51832, 6]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OA(81¹², 25923, F₈₁, 5) (dual of [25923, 25911, 6]-code), using

discarding factors / shortening the dual code based on linear OA(81¹², 25924, F₈₁, 5) (dual of [25924, 25912, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(81¹, 6481, F₈₁, 1) (dual of [6481, 6480, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
  2. linear OA(81¹, 6481, F₈₁, 1) (dual of [6481, 6480, 2]-code) (see above)
  3. linear OA(81³, 6481, F₈₁, 2) (dual of [6481, 6478, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
      - Hamming code H(3,81) [i]
  4. linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
    - a code by Danev and Olsson [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(81⁴⁹, 2110111, F₈₁, 4, 10) (dual of [(2110111, 4), 8440395, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁵³, 2110111, F₈₁, 4, 11) (dual of [(2110111, 4), 8440391, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
3	Linear OOA(81¹², 12961, F₈₁, 5, 5) (dual of [(12961, 5), 64793, 6]-NRT-code)	[i]		Appending kth Column