MinT - Information on Result #1083019

Information on Result #1083019

Linear OOA(128⁶⁸, 4227322, F₁₂₈, 4, 11) (dual of [(4227322, 4), 16909220, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁷, 4194301, F₁₂₈, 4, 5) (dual of [(4194301, 4), 16777187, 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(128⁵¹, 2113661, F₁₂₈, 4, 11) (dual of [(2113661, 4), 8454593, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128¹⁰, 16511, F₁₂₈, 4, 5) (dual of [(16511, 4), 66034, 6]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(128¹⁰, 16512, F₁₂₈, 2, 5) (dual of [(16512, 2), 33014, 6]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 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, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 2, 0) (dual of [(129, 2), 258, 1]-NRT-code) (see above)
        linear OOA(128¹, 129, F₁₂₈, 2, 1) (dual of [(129, 2), 257, 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, 129, F₁₂₈, 2, 1) (dual of [(129, 2), 257, 2]-NRT-code) (see above)
        linear OOA(128¹, 129, F₁₂₈, 2, 1) (dual of [(129, 2), 257, 2]-NRT-code) (see above)
        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(128⁵, 129, F₁₂₈, 2, 5) (dual of [(129, 2), 253, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;253,128) [i]
  2. linear OOA(128⁴¹, 2097150, F₁₂₈, 4, 11) (dual of [(2097150, 4), 8388559, 12]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(128⁴¹, 8388600, F₁₂₈, 11) (dual of [8388600, 8388559, 12]-code), using
      - discarding factors / shortening the dual code 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.