MinT - Information on Result #1621180

Information on Result #1621180

Linear OOA(3²²⁰, 2097170, F₃, 5, 20) (dual of [(2097170, 5), 10485630, 21]-NRT-code), using OOA 2-folding based on linear OOA(3²²⁰, 4194340, F₃, 3, 20) (dual of [(4194340, 3), 12582800, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²⁰, 4194341, F₃, 3, 20) (dual of [(4194341, 3), 12582803, 21]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²²⁰, 4194341, F₃, 2, 20) (dual of [(4194341, 2), 8388462, 21]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3²⁴, 40, F₃, 2, 10) (dual of [(40, 2), 56, 11]-NRT-code), using
      - extracting embedded OOA [i] based on digital (14, 24, 40)-net over F₃, using
        trace code for nets [i] based on digital (2, 12, 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(3¹⁹⁶, 4194301, F₃, 2, 20) (dual of [(4194301, 2), 8388406, 21]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(3¹⁹⁶, 8388602, F₃, 20) (dual of [8388602, 8388406, 21]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹⁹⁶, large, F₃, 20) (dual of [large, large−196, 21]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Mode: 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.