MinT - Information on Result #1150930

Information on Result #1150930

Linear OOA(2²³⁴, 2097152, F₂, 7, 14) (dual of [(2097152, 7), 14679830, 15]-NRT-code), using OOA 2-folding based on linear OOA(2²³⁴, 4194304, F₂, 4, 14) (dual of [(4194304, 4), 16776982, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁴, 4194305, F₂, 4, 14) (dual of [(4194305, 4), 16776986, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁶⁵, 2097150, F₂, 4, 7) (dual of [(2097150, 4), 8388535, 8]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
      - OOAs constructed from BCH codes [i]
  2. linear OOA(2¹⁶⁹, 2097155, F₂, 4, 14) (dual of [(2097155, 4), 8388451, 15]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁸, 5, F₂, 4, 7) (dual of [(5, 4), 12, 8]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,12P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(2¹⁶¹, 2097150, F₂, 4, 14) (dual of [(2097150, 4), 8388439, 15]-NRT-code), using
        OOA 4-folding [i] based on linear OA(2¹⁶¹, 8388600, F₂, 14) (dual of [8388600, 8388439, 15]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.