MinT - Information on Result #1084856

Information on Result #1084856

Linear OOA(128⁶², 4653439, F₁₂₈, 4, 11) (dual of [(4653439, 4), 18613694, 12]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 4, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128⁰, 32513, F₁₂₈, 4, 0) (dual of [(32513, 4), 130052, 1]-NRT-code) (see above)
linear OOA(128¹, 32513, F₁₂₈, 4, 1) (dual of [(32513, 4), 130051, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 4, 1) for arbitrarily large s, using
  - appending 3 arbitrary columns [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, 32513, F₁₂₈, 4, 1) (dual of [(32513, 4), 130051, 2]-NRT-code) (see above)
linear OOA(128¹, 32513, F₁₂₈, 4, 1) (dual of [(32513, 4), 130051, 2]-NRT-code) (see above)
linear OOA(128¹, 32513, F₁₂₈, 4, 1) (dual of [(32513, 4), 130051, 2]-NRT-code) (see above)
linear OOA(128¹, 32513, F₁₂₈, 4, 1) (dual of [(32513, 4), 130051, 2]-NRT-code) (see above)
linear OOA(128¹, 32513, F₁₂₈, 4, 1) (dual of [(32513, 4), 130051, 2]-NRT-code) (see above)
linear OOA(128⁴, 32513, F₁₂₈, 4, 2) (dual of [(32513, 4), 130048, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁴, 2113665, F₁₂₈, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
  - appending 2 arbitrary columns [i] based on linear OOA(128⁴, 2113665, F₁₂₈, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(128⁴, 2113665, F₁₂₈, 2) (dual of [2113665, 2113661, 3]-code), using
      - Hamming code H(4,128) [i]
linear OOA(128⁴, 32513, F₁₂₈, 4, 2) (dual of [(32513, 4), 130048, 3]-NRT-code) (see above)
linear OOA(128⁵, 32513, F₁₂₈, 4, 3) (dual of [(32513, 4), 130047, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁵, 49156, F₁₂₈, 4, 3) (dual of [(49156, 4), 196619, 4]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(128⁵, 49156, F₁₂₈, 3, 3) (dual of [(49156, 3), 147463, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(128⁵, 49156, F₁₂₈, 2, 3) (dual of [(49156, 2), 98307, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁵, 49156, F₁₂₈, 3) (dual of [49156, 49151, 4]-code or 49156-cap in PG(4,128)), using
        large caps in PG(4,Â b) [i]
linear OOA(128¹², 32513, F₁₂₈, 4, 5) (dual of [(32513, 4), 130040, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] 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 (see above)
      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]
linear OOA(128³¹, 524288, F₁₂₈, 4, 11) (dual of [(524288, 4), 2097121, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(128³¹, 2097152, F₁₂₈, 11) (dual of [2097152, 2097121, 12]-code), using
  - an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.