MinT - Information on Result #1165724

Information on Result #1165724

Linear OOA(2²⁵⁹, 1048592, F₂, 8, 20) (dual of [(1048592, 8), 8388477, 21]-NRT-code), using OOA 2-folding based on linear OOA(2²⁵⁹, 2097184, F₂, 4, 20) (dual of [(2097184, 4), 8388477, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁵⁹, 2097185, F₂, 4, 20) (dual of [(2097185, 4), 8388481, 21]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁹, 35, F₂, 4, 10) (dual of [(35, 4), 111, 11]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁹, 14, F₂, 4, 5) (dual of [(14, 4), 47, 6]-NRT-code), using
        extracting embedded OOA [i] based on digital (4, 9, 14)-net over F₂, using
        linear code embedding found in a computer search [i]
      2. linear OOA(2²⁰, 21, F₂, 4, 10) (dual of [(21, 4), 64, 11]-NRT-code), using
        extracting embedded OOA [i] based on digital (10, 20, 21)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²³⁰, 2097150, F₂, 4, 20) (dual of [(2097150, 4), 8388370, 21]-NRT-code), using
    - OOA 4-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: 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.