MinT - Information on Result #1060322

Information on Result #1060322

Linear OOA(3¹⁸⁶, 2097170, F₃, 4, 17) (dual of [(2097170, 4), 8388494, 18]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁸⁶, 4194340, F₃, 2, 17) (dual of [(4194340, 2), 8388494, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁸⁶, 4194341, F₃, 2, 17) (dual of [(4194341, 2), 8388496, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3²⁰, 40, F₃, 2, 8) (dual of [(40, 2), 60, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 20, 40)-net over F₃, using
      - trace code for nets [i] based on digital (2, 10, 20)-net over F₉, using
        net from sequence [i] based on digital (2, 19)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
        a function field by GarcÃa and Quoos [i]
  2. linear OOA(3¹⁶⁶, 4194301, F₃, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁶⁶, 8388602, F₃, 17) (dual of [8388602, 8388436, 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.

Other Results with Identical Parameters

None.

Depending Results

None.