MinT - Information on Result #1213290

Information on Result #1213290

Digital (91, 100, 4196253)-net over F₅, using (u,Â u+v)-construction based on

digital (14, 18, 1953)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹⁸, 1953, F₅, 4, 4) (dual of [(1953, 4), 7794, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(5¹⁸, 1953, F₅, 3, 4) (dual of [(1953, 3), 5841, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(5¹⁸, 3906, F₅, 4) (dual of [3906, 3888, 5]-code), using
      - the BCH-code C(I) with length 3906Â | 5⁶âˆ’1, defining interval IÂ =Â {1952,2343,2734,3125}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
digital (73, 82, 4194300)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁸², 4194300, F₅, 10, 9) (dual of [(4194300, 10), 41942918, 10]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(5⁸², 8388601, F₅, 2, 9) (dual of [(8388601, 2), 16777120, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5⁸², 8388602, F₅, 2, 9) (dual of [(8388602, 2), 16777122, 10]-NRT-code), using
      - trace code [i] based on linear OOA(25⁴¹, 4194301, F₂₅, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
        OOA 2-folding [i] based on linear OA(25⁴¹, 8388602, F₂₅, 9) (dual of [8388602, 8388561, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁴¹, large, F₂₅, 9) (dual of [large, large−41, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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.