MinT - Information on Result #1084878

Information on Result #1084878

Linear OOA(128²⁹, large, F₁₂₈, 4, 6), using generalized (u,Â u+v)-construction based on

linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 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, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128⁰, 699051, F₁₂₈, 4, 0) (dual of [(699051, 4), 2796204, 1]-NRT-code) (see above)
linear OOA(128¹, 699051, F₁₂₈, 4, 1) (dual of [(699051, 4), 2796203, 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, 699051, F₁₂₈, 4, 1) (dual of [(699051, 4), 2796203, 2]-NRT-code) (see above)
linear OOA(128¹, 699051, F₁₂₈, 4, 1) (dual of [(699051, 4), 2796203, 2]-NRT-code) (see above)
linear OOA(128⁴, 699051, F₁₂₈, 4, 2) (dual of [(699051, 4), 2796200, 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(128⁶, 699051, F₁₂₈, 4, 3) (dual of [(699051, 4), 2796198, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁶, 2130050, F₁₂₈, 4, 3) (dual of [(2130050, 4), 8520194, 4]-NRT-code), using
  - appending 1 arbitrary column [i] based on linear OOA(128⁶, 2130050, F₁₂₈, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(128⁶, 2130050, F₁₂₈, 2, 3) (dual of [(2130050, 2), 4260094, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁶, 2130050, F₁₂₈, 3) (dual of [2130050, 2130044, 4]-code or 2130050-cap in PG(5,128)), using
        large caps in PG(5,Â b) [i]
linear OOA(128¹⁶, 699051, F₁₂₈, 4, 6) (dual of [(699051, 4), 2796188, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(128¹⁶, 2097153, F₁₂₈, 6) (dual of [2097153, 2097137, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(128¹⁶, 2097155, F₁₂₈, 6) (dual of [2097155, 2097139, 7]-code), using
    - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
      1. linear OA(128¹⁶, 2097152, F₁₂₈, 6) (dual of [2097152, 2097136, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. linear OA(128¹³, 2097152, F₁₂₈, 5) (dual of [2097152, 2097139, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(128²⁹, large, F₁₂₈, 4, 5)	[i]	Strength Reduction for OOAs
2	Linear OOA(128²⁹, large, F₁₂₈, 4, 4)	[i]
3	Linear OOA(128²⁹, large, F₁₂₈, 4, 3)	[i]
4	Linear OOA(128³⁷, large, F₁₂₈, 4, 6)	[i]	NRT-Code Embedding in Larger Space
5	Linear OOA(128⁴¹, large, F₁₂₈, 4, 6)	[i]
6	Linear OOA(128⁴⁵, large, F₁₂₈, 4, 6)	[i]
7	Linear OOA(128⁴⁹, large, F₁₂₈, 4, 6)	[i]
8	Linear OOA(128⁵³, large, F₁₂₈, 4, 6)	[i]
9	Linear OOA(128⁶⁵, large, F₁₂₈, 4, 6)	[i]
10	Linear OOA(128⁶⁹, large, F₁₂₈, 4, 6)	[i]
11	Linear OOA(128⁷³, large, F₁₂₈, 4, 6)	[i]
12	Linear OOA(128⁷⁷, large, F₁₂₈, 4, 6)	[i]
13	Linear OOA(128³⁰, large, F₁₂₈, 4, 6)	[i]	OOA Duplication
14	Linear OOA(128³¹, large, F₁₂₈, 4, 6)	[i]	OOA Duplication