MinT - Information on Result #1165603

Information on Result #1165603

Linear OOA(2²³⁴, 1048593, F₂, 8, 19) (dual of [(1048593, 8), 8388510, 20]-NRT-code), using OOA 2-folding based on linear OOA(2²³⁴, 2097186, F₂, 4, 19) (dual of [(2097186, 4), 8388510, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁴, 2097187, F₂, 4, 19) (dual of [(2097187, 4), 8388514, 20]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁶, 37, F₂, 4, 9) (dual of [(37, 4), 122, 10]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁸, 17, F₂, 4, 4) (dual of [(17, 4), 60, 5]-NRT-code), using
        appending kth column [i] based on linear OOA(2⁸, 17, F₂, 3, 4) (dual of [(17, 3), 43, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (4, 8, 17)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
      2. linear OOA(2¹⁸, 20, F₂, 4, 9) (dual of [(20, 4), 62, 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, 2097150, F₂, 4, 19) (dual of [(2097150, 4), 8388392, 20]-NRT-code), using
    - OOA 4-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: 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.