MinT - Information on Result #1184010

Information on Result #1184010

Digital (188, 202, 2097153)-net over F₃, using net defined by OOA based on linear OOA(3²⁰², 2097153, F₃, 20, 14) (dual of [(2097153, 20), 41942858, 15]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(3²⁰², 4194307, F₃, 4, 14) (dual of [(4194307, 4), 16777026, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁰², 4194308, F₃, 4, 14) (dual of [(4194308, 4), 16777030, 15]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3⁸, 7, F₃, 4, 7) (dual of [(7, 4), 20, 8]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,20P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(3¹⁹⁴, 4194301, F₃, 4, 14) (dual of [(4194301, 4), 16777010, 15]-NRT-code), using
      - OOA 2-folding [i] based on linear OOA(3¹⁹⁴, 8388602, F₃, 2, 14) (dual of [(8388602, 2), 16777010, 15]-NRT-code), using
        trace code [i] based on linear OOA(9⁹⁷, 4194301, F₉, 2, 14) (dual of [(4194301, 2), 8388505, 15]-NRT-code), using
        OOA 2-folding [i] based on linear OA(9⁹⁷, 8388602, F₉, 14) (dual of [8388602, 8388505, 15]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁹⁷, large, F₉, 14) (dual of [large, large−97, 15]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 9⁸âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.