MinT - Information on Result #1184398

Information on Result #1184398

Digital (158, 175, 1048578)-net over F₃, using net defined by OOA based on linear OOA(3¹⁷⁵, 1048578, F₃, 20, 17) (dual of [(1048578, 20), 20971385, 18]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(3¹⁷⁵, 2097157, F₃, 4, 17) (dual of [(2097157, 4), 8388453, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁹, 7, F₃, 4, 8) (dual of [(7, 4), 19, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,19P) [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(3¹⁶⁶, 2097150, F₃, 4, 17) (dual of [(2097150, 4), 8388434, 18]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(3¹⁶⁶, 8388600, F₃, 17) (dual of [8388600, 8388434, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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.