MinT - Information on Result #1672285

Information on Result #1672285

Linear OOA(2²⁵⁷, 1584865, F₂, 6, 20) (dual of [(1584865, 6), 9508933, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁵⁷, 1584865, F₂, 5, 20) (dual of [(1584865, 5), 7924068, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁵⁷, 1677750, F₂, 5, 20) (dual of [(1677750, 5), 8388493, 21]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁷, 30, F₂, 5, 10) (dual of [(30, 5), 123, 11]-NRT-code), using
    - extracting embedded OOA [i] based on digital (17, 27, 30)-net over F₂, using
      - 3 times m-reduction [i] based on digital (17, 30, 30)-net over F₂, using
        a shift-net [i]
  2. linear OOA(2²³⁰, 1677720, F₂, 5, 20) (dual of [(1677720, 5), 8388370, 21]-NRT-code), using
    - OOA 5-folding [i] based on linear OA(2²³⁰, 8388600, F₂, 20) (dual of [8388600, 8388370, 21]-code), using
      - discarding factors / shortening the dual code based on linear OA(2²³⁰, large, F₂, 20) (dual of [large, large−230, 21]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Mode: 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.