MinT - Information on Result #1192436

Information on Result #1192436

Digital (137, 158, 838864)-net over F₈, using net defined by OOA based on linear OOA(8¹⁵⁸, 838864, F₈, 22, 21) (dual of [(838864, 22), 18454850, 22]-NRT-code), using

OOA 5-folding and stacking with additional row [i] based on linear OOA(8¹⁵⁸, 4194321, F₈, 2, 21) (dual of [(4194321, 2), 8388484, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8¹⁵⁸, 4194325, F₈, 2, 21) (dual of [(4194325, 2), 8388492, 22]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(8¹³, 24, F₈, 2, 10) (dual of [(24, 2), 35, 11]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,37P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
        the Klein quartic over F₈ [i]
    2. linear OOA(8¹⁴⁵, 4194301, F₈, 2, 21) (dual of [(4194301, 2), 8388457, 22]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(8¹⁴⁵, 8388602, F₈, 21) (dual of [8388602, 8388457, 22]-code), using
        discarding factors / shortening the dual code based on linear OA(8¹⁴⁵, large, F₈, 21) (dual of [large, large−145, 22]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 8¹⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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.