MinT - Information on Result #1013191

Information on Result #1013191

Linear OOA(5¹²⁴, 4194353, F₅, 3, 12) (dual of [(4194353, 3), 12582935, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹², 52, F₅, 3, 6) (dual of [(52, 3), 144, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 12, 52)-net over F₅, using
  - trace code for nets [i] based on digital (0, 6, 26)-net over F₂₅, using
    - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
      - Niederreiter sequence [i]
linear OOA(5¹¹², 4194301, F₅, 3, 12) (dual of [(4194301, 3), 12582791, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(5¹¹², 8388602, F₅, 2, 12) (dual of [(8388602, 2), 16777092, 13]-NRT-code), using
  - trace code [i] based on linear OOA(25⁵⁶, 4194301, F₂₅, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25⁵⁶, 8388602, F₂₅, 12) (dual of [8388602, 8388546, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(25⁵⁶, large, F₂₅, 12) (dual of [large, large−56, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.