MinT - Information on Result #1131622

Information on Result #1131622

Linear OOA(2²³⁴, 1398120, F₂, 6, 18) (dual of [(1398120, 6), 8388486, 19]-NRT-code), using OOA 2-folding based on linear OOA(2²³⁴, 2796240, F₂, 3, 18) (dual of [(2796240, 3), 8388486, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁴, 2796241, F₂, 3, 18) (dual of [(2796241, 3), 8388489, 19]-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(2²⁰⁷, 2796201, F₂, 3, 18) (dual of [(2796201, 3), 8388396, 19]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2²⁰⁷, large, F₂, 18) (dual of [large, large−207, 19]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.