MinT - Information on Result #1758267

Information on Result #1758267

Digital (219, 238, 1408589)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁸, 1408589, F₂, 5, 19) (dual of [(1408589, 5), 7042707, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁸, 1677772, F₂, 5, 19) (dual of [(1677772, 5), 8388622, 20]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2³⁰, 52, F₂, 5, 9) (dual of [(52, 5), 230, 10]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2¹⁰, 32, F₂, 5, 4) (dual of [(32, 5), 150, 5]-NRT-code), using
        appending 1 arbitrary column [i] based on linear OOA(2¹⁰, 32, F₂, 4, 4) (dual of [(32, 4), 118, 5]-NRT-code), using
        appending kth column [i] based on linear OOA(2¹⁰, 32, F₂, 3, 4) (dual of [(32, 3), 86, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 10, 32)-net over F₂, using
        linear code embedding found in a computer search [i]
      2. linear OOA(2²⁰, 26, F₂, 5, 9) (dual of [(26, 5), 110, 10]-NRT-code), using
        extracting embedded OOA [i] based on digital (11, 20, 26)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²⁰⁸, 1677720, F₂, 5, 19) (dual of [(1677720, 5), 8388392, 20]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2²⁰⁸, 8388600, F₂, 19) (dual of [8388600, 8388392, 20]-code), using
      - discarding factors / shortening the dual code based on linear OA(2²⁰⁸, large, F₂, 19) (dual of [large, large−208, 20]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]

Mode: 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.