MinT - Information on Result #907117

Information on Result #907117

Linear OOA(128¹⁵, 1056896, F₁₂₈, 2, 5) (dual of [(1056896, 2), 2113777, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
linear OOA(128¹, 8257, F₁₂₈, 2, 1) (dual of [(8257, 2), 16513, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(128¹, 8257, F₁₂₈, 2, 1) (dual of [(8257, 2), 16513, 2]-NRT-code) (see above)
linear OOA(128¹, 8257, F₁₂₈, 2, 1) (dual of [(8257, 2), 16513, 2]-NRT-code) (see above)
linear OOA(128³, 8257, F₁₂₈, 2, 2) (dual of [(8257, 2), 16511, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128³, 16513, F₁₂₈, 2, 2) (dual of [(16513, 2), 33023, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
    - Hamming code H(3,128) [i]
linear OOA(128⁹, 8257, F₁₂₈, 2, 5) (dual of [(8257, 2), 16505, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128², 129, F₁₂₈, 2, 2) (dual of [(129, 2), 256, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;256,128) [i]
  2. linear OOA(128⁷, 8128, F₁₂₈, 2, 5) (dual of [(8128, 2), 16249, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(128⁷, 16256, F₁₂₈, 5) (dual of [16256, 16249, 6]-code), using
      - discarding factors / shortening the dual code based on 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		Method
1	Linear OOA(128⁵⁶, 5251197, F₁₂₈, 2, 11) (dual of [(5251197, 2), 10502338, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(128⁵², 5251197, F₁₂₈, 2, 10) (dual of [(5251197, 2), 10502342, 11]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(128¹⁵, 1056895, F₁₂₈, 3, 5) (dual of [(1056895, 3), 3170670, 6]-NRT-code)	[i]	OOA Stacking with Additional Row
4	Linear OOA(128¹⁵, 1056895, F₁₂₈, 4, 5) (dual of [(1056895, 4), 4227565, 6]-NRT-code)	[i]	OOA Stacking with Additional Row