MinT - Information on Result #1022681

Information on Result #1022681

Linear OOA(128¹⁶, large, F₁₂₈, 3, 4), using generalized (u,Â u+v)-construction based on

linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 3, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128⁰, 1048577, F₁₂₈, 3, 0) (dual of [(1048577, 3), 3145731, 1]-NRT-code) (see above)
linear OOA(128¹, 1048577, F₁₂₈, 3, 1) (dual of [(1048577, 3), 3145730, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 3, 1) for arbitrarily large s, using
  - appending 2 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, 1048577, F₁₂₈, 3, 1) (dual of [(1048577, 3), 3145730, 2]-NRT-code) (see above)
linear OOA(128⁴, 1048577, F₁₂₈, 3, 2) (dual of [(1048577, 3), 3145727, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁴, 2113665, F₁₂₈, 3, 2) (dual of [(2113665, 3), 6340991, 3]-NRT-code), using
  - appending 1 arbitrary column [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(128¹⁰, 1048577, F₁₂₈, 3, 4) (dual of [(1048577, 3), 3145721, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(128¹⁰, 2097154, F₁₂₈, 4) (dual of [2097154, 2097144, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(128¹⁰, 2097155, F₁₂₈, 4) (dual of [2097155, 2097145, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(128¹⁰, 2097152, F₁₂₈, 4) (dual of [2097152, 2097142, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(128⁷, 2097152, F₁₂₈, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
      3. linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(128¹⁶, large, F₁₂₈, 3, 3)	[i]	Strength Reduction for OOAs
2	Linear OOA(128¹⁹, large, F₁₂₈, 3, 4)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(128²⁵, large, F₁₂₈, 3, 4)	[i]
4	Linear OOA(128²⁸, large, F₁₂₈, 3, 4)	[i]
5	Linear OOA(128³¹, large, F₁₂₈, 3, 4)	[i]
6	Linear OOA(128³⁷, large, F₁₂₈, 3, 4)	[i]
7	Linear OOA(128⁴⁰, large, F₁₂₈, 3, 4)	[i]
8	Linear OOA(128⁴³, large, F₁₂₈, 3, 4)	[i]
9	Linear OOA(128⁴⁶, large, F₁₂₈, 3, 4)	[i]
10	Linear OOA(128⁴⁹, large, F₁₂₈, 3, 4)	[i]
11	Linear OOA(128⁵², large, F₁₂₈, 3, 4)	[i]
12	Linear OOA(128⁵⁸, large, F₁₂₈, 3, 4)	[i]
13	Linear OOA(128⁶¹, large, F₁₂₈, 3, 4)	[i]
14	Linear OOA(128⁶⁷, large, F₁₂₈, 3, 4)	[i]
15	Linear OOA(128⁷³, large, F₁₂₈, 3, 4)	[i]
16	Linear OOA(128⁷⁶, large, F₁₂₈, 3, 4)	[i]
17	Linear OOA(128¹⁷, large, F₁₂₈, 3, 4)	[i]	OOA Duplication
18	Linear OOA(128¹⁶, large, F₁₂₈, 4, 4)	[i]	Appending kth Column