MinT - Information on Result #1131750

Information on Result #1131750

Linear OOA(2²³⁵, 1398120, F₂, 6, 19) (dual of [(1398120, 6), 8388485, 20]-NRT-code), using OOA 2-folding based on linear OOA(2²³⁵, 2796240, F₂, 3, 19) (dual of [(2796240, 3), 8388485, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁵, 2796241, F₂, 3, 19) (dual of [(2796241, 3), 8388488, 20]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁷, 40, F₂, 3, 9) (dual of [(40, 3), 93, 10]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁹, 23, F₂, 3, 4) (dual of [(23, 3), 60, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (5, 9, 23)-net over F₂, using
        linear code embedding found in a computer search [i]
      2. linear OOA(2¹⁸, 20, F₂, 3, 9) (dual of [(20, 3), 42, 10]-NRT-code), using
        extracting embedded OOA [i] based on digital (9, 18, 20)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²⁰⁸, 2796201, F₂, 3, 19) (dual of [(2796201, 3), 8388395, 20]-NRT-code), using
    - OOA 3-folding [i] 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: 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.