MinT - Information on Result #3259691

Information on Result #3259691

Digital (50, 54, large)-net over F₅, using 5⁸ times duplication based on digital (42, 46, large)-net over F₅, using

t-expansion [i] based on digital (41, 46, large)-net over F₅, using
- trace code for nets [i] based on digital (18, 23, 4194326)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25²³, 4194326, F₂₅, 6, 5) (dual of [(4194326, 6), 25165933, 6]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(25²³, 4194327, F₂₅, 2, 5) (dual of [(4194327, 2), 8388631, 6]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(25², 26, F₂₅, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;50,25) [i]
        linear OOA(25²¹, 4194301, F₂₅, 2, 5) (dual of [(4194301, 2), 8388581, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(25²¹, 8388602, F₂₅, 5) (dual of [8388602, 8388581, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(25²¹, large, F₂₅, 5) (dual of [large, large−21, 6]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.