MinT - Information on Result #1213446

Information on Result #1213446

Digital (113, 124, 3358444)-net over F₅, using (u,Â u+v)-construction based on

digital (17, 22, 3004)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5²², 3004, F₅, 6, 5) (dual of [(3004, 6), 18002, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(5²², 3005, F₅, 2, 5) (dual of [(3005, 2), 5988, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(5¹, 601, F₅, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OOA(5¹, 601, F₅, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code) (see above)
      3. linear OOA(5¹, 601, F₅, 2, 1) (dual of [(601, 2), 1201, 2]-NRT-code) (see above)
      4. linear OOA(5⁵, 601, F₅, 2, 2) (dual of [(601, 2), 1197, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(5⁵, 781, F₅, 2, 2) (dual of [(781, 2), 1557, 3]-NRT-code), using
        appending kth column [i] based on linear OA(5⁵, 781, F₅, 2) (dual of [781, 776, 3]-code), using
        Hamming code H(5,5) [i]
      5. linear OOA(5¹⁴, 601, F₅, 2, 5) (dual of [(601, 2), 1188, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(5¹⁴, 1202, F₅, 5) (dual of [1202, 1188, 6]-code), using
        trace code [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
        a code by Danev and Olsson [i]
digital (91, 102, 3355440)-net over F₅, using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25⁵¹, 1677720, F₂₅, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(25⁵¹, 8388601, F₂₅, 11) (dual of [8388601, 8388550, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁵¹, large, F₂₅, 11) (dual of [large, large−51, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.