MinT - Information on Result #1130379

Information on Result #1130379

Linear OOA(2¹⁴⁵, 4194305, F₂, 6, 10) (dual of [(4194305, 6), 25165685, 11]-NRT-code), using OOA stacking with additional row based on linear OOA(2¹⁴⁵, 4194306, F₂, 5, 10) (dual of [(4194306, 5), 20971385, 11]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶, 5, F₂, 5, 5) (dual of [(5, 5), 19, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(2⁶, 5, F₂, 4, 5) (dual of [(5, 4), 14, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,14P) [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(2¹³⁹, 4194301, F₂, 5, 10) (dual of [(4194301, 5), 20971366, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹³⁹, 8388602, F₂, 3, 10) (dual of [(8388602, 3), 25165667, 11]-NRT-code), using
    - 1 step truncation [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
      - OOAs constructed from BCH codes [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.