MinT - Information on Result #1117557

Information on Result #1117557

Linear OOA(3²³³, 4194385, F₃, 5, 14) (dual of [(4194385, 5), 20971692, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3²¹, 84, F₃, 5, 7) (dual of [(84, 5), 399, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (14, 21, 84)-net over F₃, using
  - trace code for nets [i] based on digital (0, 7, 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]
linear OOA(3²¹², 4194301, F₃, 5, 14) (dual of [(4194301, 5), 20971293, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3²¹², 8388602, F₃, 3, 14) (dual of [(8388602, 3), 25165594, 15]-NRT-code), using
  - trace code [i] based on linear OOA(9¹⁰⁶, 4194301, F₉, 3, 14) (dual of [(4194301, 3), 12582797, 15]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(9¹⁰⁶, 8388602, F₉, 2, 14) (dual of [(8388602, 2), 16777098, 15]-NRT-code), using
      - trace code [i] based on linear OOA(81⁵³, 4194301, F₈₁, 2, 14) (dual of [(4194301, 2), 8388549, 15]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁵³, 8388602, F₈₁, 14) (dual of [8388602, 8388549, 15]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁵³, large, F₈₁, 14) (dual of [large, large−53, 15]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.