MinT - Information on Result #1187006

Information on Result #1187006

Digital (182, 202, 838869)-net over F₄, using net defined by OOA based on linear OOA(4²⁰², 838869, F₄, 22, 20) (dual of [(838869, 22), 18454916, 21]-NRT-code), using

OOA 5-folding and stacking with additional row [i] based on linear OOA(4²⁰², 4194346, F₄, 2, 20) (dual of [(4194346, 2), 8388490, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²⁰², 4194349, F₄, 2, 20) (dual of [(4194349, 2), 8388496, 21]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(4²², 48, F₄, 2, 10) (dual of [(48, 2), 74, 11]-NRT-code), using
      - extracting embedded OOA [i] based on digital (12, 22, 48)-net over F₄, using
        trace code for nets [i] based on digital (1, 11, 24)-net over F₁₆, using
        net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
    2. linear OOA(4¹⁸⁰, 4194301, F₄, 2, 20) (dual of [(4194301, 2), 8388422, 21]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(4¹⁸⁰, 8388602, F₄, 20) (dual of [8388602, 8388422, 21]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹⁸⁰, large, F₄, 20) (dual of [large, large−180, 21]-code), using
        the primitive narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.