MinT - Information on Result #1691153

Information on Result #1691153

Linear OOA(2¹⁹⁹, 2099197, F₂, 8, 15) (dual of [(2099197, 8), 16793377, 16]-NRT-code), using OOA stacking with additional row based on linear OOA(2¹⁹⁹, 2099198, F₂, 7, 15) (dual of [(2099198, 7), 14694187, 16]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁹⁹, 2099198, F₂, 4, 15) (dual of [(2099198, 4), 8396593, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2³⁵, 2047, F₂, 4, 7) (dual of [(2047, 4), 8153, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (28, 35, 2047)-net over F₂, using
      - nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(2¹⁶⁴, 2097151, F₂, 4, 15) (dual of [(2097151, 4), 8388440, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(2¹⁶⁴, 4194302, F₂, 2, 15) (dual of [(4194302, 2), 8388440, 16]-NRT-code), using
      - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁶², 4194301, F₂, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
        OOA 2-folding [i] based on linear OA(2¹⁶², 8388602, F₂, 15) (dual of [8388602, 8388440, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: 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.