MinT - Information on Result #1019214

Information on Result #1019214

Linear OOA(128⁷³, 7706192, F₁₂₈, 3, 11) (dual of [(7706192, 3), 23118503, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁷, 4194301, F₁₂₈, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(128¹⁷, large, F₁₂₈, 5) (dual of [large, large−17, 6]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
linear OOA(128⁵⁶, 3853096, F₁₂₈, 3, 11) (dual of [(3853096, 3), 11559232, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128¹⁵, 1056895, F₁₂₈, 3, 5) (dual of [(1056895, 3), 3170670, 6]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(128¹⁵, 1056896, F₁₂₈, 2, 5) (dual of [(1056896, 2), 2113777, 6]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] 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
        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]
        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]
  2. linear OOA(128⁴¹, 2796201, F₁₂₈, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(128⁴¹, large, F₁₂₈, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.