MinT - Information on Result #1189072

Information on Result #1189072

Digital (127, 143, 1048601)-net over F₅, using net defined by OOA based on linear OOA(5¹⁴³, 1048601, F₅, 18, 16) (dual of [(1048601, 18), 18874675, 17]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(5¹⁴³, 4194405, F₅, 2, 16) (dual of [(4194405, 2), 8388667, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5²², 104, F₅, 2, 8) (dual of [(104, 2), 186, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (14, 22, 104)-net over F₅, using
      - trace code for nets [i] based on digital (3, 11, 52)-net over F₂₅, using
        net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
        a function field by GarcÃa and Quoos [i]
  2. linear OOA(5¹²¹, 4194301, F₅, 2, 16) (dual of [(4194301, 2), 8388481, 17]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(5¹²¹, 8388602, F₅, 16) (dual of [8388602, 8388481, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(5¹²¹, large, F₅, 16) (dual of [large, large−121, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.