MinT - Information on Result #873723

Information on Result #873723

Linear OOA(64¹², 8066, F₆₄, 2, 5) (dual of [(8066, 2), 16120, 6]-NRT-code), using OOA 2-folding 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, 4202367, F₆₄, 2, 10) (dual of [(4202367, 2), 8404685, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(64⁵³, 4202367, F₆₄, 2, 11) (dual of [(4202367, 2), 8404681, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs