MinT - Information on Result #1203836

Information on Result #1203836

Digital (50, 69, 233109)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁶⁹, 233109, F₁₂₈, 21, 19) (dual of [(233109, 21), 4895220, 20]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(128⁶⁹, 699328, F₁₂₈, 3, 19) (dual of [(699328, 3), 2097915, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128⁶⁹, 699330, F₁₂₈, 3, 19) (dual of [(699330, 3), 2097921, 20]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(128¹⁴, 279, F₁₂₈, 3, 9) (dual of [(279, 3), 823, 10]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(128⁴, 129, F₁₂₈, 3, 4) (dual of [(129, 3), 383, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;383,128) [i]
        linear OOA(128¹⁰, 150, F₁₂₈, 3, 9) (dual of [(150, 3), 440, 10]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,440P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
        a function field by SÃ©mirat [i]
    2. linear OOA(128⁵⁵, 699051, F₁₂₈, 3, 19) (dual of [(699051, 3), 2097098, 20]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(128⁵⁵, 2097153, F₁₂₈, 19) (dual of [2097153, 2097098, 20]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.