MinT - Information on Result #1203114

Information on Result #1203114

Digital (17, 24, 748206)-net over F₁₂₈, using net defined by OOA based on linear OOA(128²⁴, 748206, F₁₂₈, 9, 7) (dual of [(748206, 9), 6733830, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(128²⁴, 748207, F₁₂₈, 3, 7) (dual of [(748207, 3), 2244597, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁵, 49156, F₁₂₈, 3, 3) (dual of [(49156, 3), 147463, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(128⁵, 49156, F₁₂₈, 2, 3) (dual of [(49156, 2), 98307, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁵, 49156, F₁₂₈, 3) (dual of [49156, 49151, 4]-code or 49156-cap in PG(4,128)), using
        large caps in PG(4,Â b) [i]
  2. linear OOA(128¹⁹, 699051, F₁₂₈, 3, 7) (dual of [(699051, 3), 2097134, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(128¹⁹, 2097153, F₁₂₈, 7) (dual of [2097153, 2097134, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (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.