MinT - Information on Result #1175701

Information on Result #1175701

Linear OOA(2²³⁷, 2396756, F₂, 8, 15) (dual of [(2396756, 8), 19173811, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097150, F₂, 8, 7) (dual of [(2097150, 8), 16777135, 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]
linear OOA(2¹⁷², 1198378, F₂, 8, 15) (dual of [(1198378, 8), 9586852, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰, 7, F₂, 8, 7) (dual of [(7, 8), 46, 8]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(2¹⁰, 7, F₂, 7, 7) (dual of [(7, 7), 39, 8]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹⁰, 7, F₂, 6, 7) (dual of [(7, 6), 32, 8]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(6;F,34P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹⁶², 1198371, F₂, 8, 15) (dual of [(1198371, 8), 9586806, 16]-NRT-code), using
    - OOA 7-folding and stacking with additional row [i] based on linear OA(2¹⁶², 8388598, F₂, 15) (dual of [8388598, 8388436, 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: 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.