MinT - Information on Result #1228117

Information on Result #1228117

Digital (29, 40, 427687)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (4, 9, 8257)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁹, 8257, F₁₂₈, 5, 5) (dual of [(8257, 5), 41276, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(128⁹, 8257, F₁₂₈, 4, 5) (dual of [(8257, 4), 33019, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(128², 129, F₁₂₈, 4, 2) (dual of [(129, 4), 514, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;514,128) [i]
      2. linear OOA(128⁷, 8128, F₁₂₈, 4, 5) (dual of [(8128, 4), 32505, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
digital (20, 31, 419430)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128³¹, 419430, F₁₂₈, 11, 11) (dual of [(419430, 11), 4613699, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(128³¹, 2097151, F₁₂₈, 11) (dual of [2097151, 2097120, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(128³¹, 2097152, F₁₂₈, 11) (dual of [2097152, 2097121, 12]-code), using
      - an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

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None.