MinT - Information on Result #2523681

Information on Result #2523681

OOA(4²⁴⁵, 4194688, S₄, 2, 23), using 4¹ times duplication based on OOA(4²⁴⁴, 4194688, S₄, 2, 23), using

(u,Â u+v)-construction [i] based on
1. OOA(4³⁹, 387, S₄, 2, 11), using
  - extracting embedded OOA [i] based on (28, 39, 387)-net in base 4, using
    - trace code for nets [i] based on (2, 13, 129)-net in base 64, using
      - 1 times m-reduction [i] based on (2, 14, 129)-net in base 64, using
        base change [i] based on digital (0, 12, 129)-net over F₁₂₈, using
        net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
        Niederreiter sequence [i]
2. linear OOA(4²⁰⁵, 4194301, F₄, 2, 23) (dual of [(4194301, 2), 8388397, 24]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²⁰⁵, 8388602, F₄, 23) (dual of [8388602, 8388397, 24]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²⁰⁵, large, F₄, 23) (dual of [large, large−205, 24]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

Mode: Constructive.

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.