MinT - Information on Result #1199590

Information on Result #1199590

Digital (77, 94, 1048594)-net over F₃₂, using net defined by OOA based on linear OOA(32⁹⁴, 1048594, F₃₂, 18, 17) (dual of [(1048594, 18), 18874598, 18]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(32⁹⁴, 4194377, F₃₂, 2, 17) (dual of [(4194377, 2), 8388660, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(32⁹⁴, 4194378, F₃₂, 2, 17) (dual of [(4194378, 2), 8388662, 18]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(32¹³, 77, F₃₂, 2, 8) (dual of [(77, 2), 141, 9]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(32⁴, 33, F₃₂, 2, 4) (dual of [(33, 2), 62, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;62,32) [i]
        linear OOA(32⁹, 44, F₃₂, 2, 8) (dual of [(44, 2), 79, 9]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,79P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
    2. linear OOA(32⁸¹, 4194301, F₃₂, 2, 17) (dual of [(4194301, 2), 8388521, 18]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(32⁸¹, 8388602, F₃₂, 17) (dual of [8388602, 8388521, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁸¹, large, F₃₂, 17) (dual of [large, large−81, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (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.