MinT - Information on Result #1060464

Information on Result #1060464

Linear OOA(3²⁰⁷, 2097192, F₃, 4, 18) (dual of [(2097192, 4), 8388561, 19]-NRT-code), using OOA 2-folding based on linear OOA(3²⁰⁷, 4194384, F₃, 2, 18) (dual of [(4194384, 2), 8388561, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁰⁷, 4194385, F₃, 2, 18) (dual of [(4194385, 2), 8388563, 19]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3²⁷, 84, F₃, 2, 9) (dual of [(84, 2), 141, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (18, 27, 84)-net over F₃, using
      - trace code for nets [i] based on digital (0, 9, 28)-net over F₂₇, using
        net from sequence [i] based on digital (0, 27)-sequence over F₂₇, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 0 and N(F) ≥ 28, using
        the rational function field F₂₇(x) [i]
        Niederreiter sequence [i]
  2. linear OOA(3¹⁸⁰, 4194301, F₃, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁸⁰, 8388602, F₃, 18) (dual of [8388602, 8388422, 19]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.