MinT - Information on Result #1183466

Information on Result #1183466

Digital (101, 112, 1677726)-net over F₃, using net defined by OOA based on linear OOA(3¹¹², 1677726, F₃, 15, 11) (dual of [(1677726, 15), 25165778, 12]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(3¹¹², 1677727, F₃, 5, 11) (dual of [(1677727, 5), 8388523, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 7, F₃, 5, 5) (dual of [(7, 5), 29, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁶, 7, F₃, 4, 5) (dual of [(7, 4), 22, 6]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,22P) [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(3¹⁰⁶, 1677720, F₃, 5, 11) (dual of [(1677720, 5), 8388494, 12]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(3¹⁰⁶, 8388600, F₃, 11) (dual of [8388600, 8388494, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁰⁶, large, F₃, 11) (dual of [large, large−106, 12]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’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.