MinT - Information on Result #1084861

Information on Result #1084861

Linear OOA(128⁵⁹, 7242232, F₁₂₈, 4, 10) (dual of [(7242232, 4), 28968869, 11]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 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, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128⁰, 49156, F₁₂₈, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
linear OOA(128¹, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 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, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
linear OOA(128¹, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
linear OOA(128¹, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
linear OOA(128¹, 49156, F₁₂₈, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
linear OOA(128⁴, 49156, F₁₂₈, 4, 2) (dual of [(49156, 4), 196620, 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, 49156, F₁₂₈, 4, 2) (dual of [(49156, 4), 196620, 3]-NRT-code) (see above)
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(128¹³, 524288, F₁₂₈, 4, 5) (dual of [(524288, 4), 2097139, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128¹³, 1048577, F₁₂₈, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(128¹³, 2097155, F₁₂₈, 5) (dual of [2097155, 2097142, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. 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]
      2. 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]
      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]
linear OOA(128²⁸, 524288, F₁₂₈, 4, 10) (dual of [(524288, 4), 2097124, 11]-NRT-code), using
- OOA 4-folding [i] based on linear OA(128²⁸, 2097152, F₁₂₈, 10) (dual of [2097152, 2097124, 11]-code), using
  - an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.