MinT - Information on Result #1180070

Information on Result #1180070

Digital (111, 122, 1677724)-net over F₂, using net defined by OOA based on linear OOA(2¹²², 1677724, F₂, 15, 11) (dual of [(1677724, 15), 25165738, 12]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2¹²², 1677725, F₂, 5, 11) (dual of [(1677725, 5), 8388503, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁶, 5, F₂, 5, 5) (dual of [(5, 5), 19, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁶, 5, F₂, 4, 5) (dual of [(5, 4), 14, 6]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,14P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹¹⁶, 1677720, F₂, 5, 11) (dual of [(1677720, 5), 8388484, 12]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2¹¹⁶, 8388600, F₂, 11) (dual of [8388600, 8388484, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹¹⁶, large, F₂, 11) (dual of [large, large−116, 12]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.