MinT - Information on Result #1164642

Information on Result #1164642

Linear OOA(2²¹⁰, 2796211, F₂, 8, 12) (dual of [(2796211, 8), 22369478, 13]-NRT-code), using OOA stacking with additional row based on linear OOA(2²¹⁰, 2796212, F₂, 6, 12) (dual of [(2796212, 6), 16777062, 13]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁴, 2097149, F₂, 6, 6) (dual of [(2097149, 6), 12582830, 7]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁶⁴, 2097150, F₂, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
    - 1 step truncation [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(2¹⁴⁶, 1398106, F₂, 6, 12) (dual of [(1398106, 6), 8388490, 13]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁸, 6, F₂, 6, 6) (dual of [(6, 6), 28, 7]-NRT-code), using
      - appending kth column [i] based on linear OOA(2⁸, 6, F₂, 5, 6) (dual of [(6, 5), 22, 7]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(5;F,23P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(2¹³⁸, 1398100, F₂, 6, 12) (dual of [(1398100, 6), 8388462, 13]-NRT-code), using
      - OOA 6-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.