MinT - Information on Result #3260113

Information on Result #3260113

Digital (133, 144, 6710880)-net over F₅, using 5² times duplication based on digital (131, 142, 6710880)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (35, 40, 4194301)-net over F₅, using
  - net defined by OOA [i] based on linear OOA(5⁴⁰, 4194301, F₅, 5, 5) (dual of [(4194301, 5), 20971465, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(5⁴⁰, large, F₅, 5) (dual of [large, large−40, 6]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
2. 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.