MinT - Information on Result #2991241

Information on Result #2991241

Linear OOA(2²³⁹, 1048633, F₂, 8, 18) (dual of [(1048633, 8), 8388825, 19]-NRT-code), using strength reduction based on linear OOA(2²³⁹, 1048633, F₂, 8, 19) (dual of [(1048633, 8), 8388825, 20]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2³¹, 58, F₂, 8, 9) (dual of [(58, 8), 433, 10]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹⁰, 32, F₂, 8, 4) (dual of [(32, 8), 246, 5]-NRT-code), using
      - appending 4 arbitrary columns [i] based on linear OOA(2¹⁰, 32, F₂, 4, 4) (dual of [(32, 4), 118, 5]-NRT-code), using
        appending kth column [i] based on linear OOA(2¹⁰, 32, F₂, 3, 4) (dual of [(32, 3), 86, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 10, 32)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2²¹, 29, F₂, 8, 9) (dual of [(29, 8), 211, 10]-NRT-code), using
      - extracting embedded OOA [i] based on digital (12, 21, 29)-net over F₂, using
        linear code embedding found in a computer search [i]
2. linear OOA(2²⁰⁸, 1048575, F₂, 8, 19) (dual of [(1048575, 8), 8388392, 20]-NRT-code), using
  - OOA 8-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.