MinT - Information on Result #944818

Information on Result #944818

Linear OOA(64¹², 8065, F₆₄, 3, 5) (dual of [(8065, 3), 24183, 6]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OA(64¹², 16131, F₆₄, 5) (dual of [16131, 16119, 6]-code), using

discarding factors / shortening the dual code based on linear OA(64¹², 16132, F₆₄, 5) (dual of [16132, 16120, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(64¹, 4033, F₆₄, 1) (dual of [4033, 4032, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
  2. linear OA(64¹, 4033, F₆₄, 1) (dual of [4033, 4032, 2]-code) (see above)
  3. linear OA(64³, 4033, F₆₄, 2) (dual of [4033, 4030, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
      - Hamming code H(3,64) [i]
  4. linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 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(64⁴⁹, 2804266, F₆₄, 3, 10) (dual of [(2804266, 3), 8412749, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(64⁵³, 2804266, F₆₄, 3, 11) (dual of [(2804266, 3), 8412745, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs