MinT - Information on Result #876265

Information on Result #876265

Linear OOA(81¹², 12962, F₈₁, 2, 5) (dual of [(12962, 2), 25912, 6]-NRT-code), using OOA 2-folding 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, 4207263, F₈₁, 2, 10) (dual of [(4207263, 2), 8414477, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁵³, 4207263, F₈₁, 2, 11) (dual of [(4207263, 2), 8414473, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs