MinT - Information on Result #944874

Information on Result #944874

Linear OOA(128¹², 32513, F₁₂₈, 3, 5) (dual of [(32513, 3), 97527, 6]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OA(128¹², 65027, F₁₂₈, 5) (dual of [65027, 65015, 6]-code), using

discarding factors / shortening the dual code based on linear OA(128¹², 65028, F₁₂₈, 5) (dual of [65028, 65016, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(128¹, 16257, F₁₂₈, 1) (dual of [16257, 16256, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
  2. linear OA(128¹, 16257, F₁₂₈, 1) (dual of [16257, 16256, 2]-code) (see above)
  3. linear OA(128³, 16257, F₁₂₈, 2) (dual of [16257, 16254, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
      - Hamming code H(3,128) [i]
  4. linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 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(128⁴⁹, 2828714, F₁₂₈, 3, 10) (dual of [(2828714, 3), 8486093, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(128⁵³, 2828714, F₁₂₈, 3, 11) (dual of [(2828714, 3), 8486089, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs