MinT - Information on Result #1164131

Information on Result #1164131

Linear OOA(2¹²⁰, 4194305, F₂, 8, 8) (dual of [(4194305, 8), 33554320, 9]-NRT-code), using OOA stacking with additional row based on linear OOA(2¹²⁰, 4194306, F₂, 4, 8) (dual of [(4194306, 4), 16777104, 9]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵, 5, F₂, 4, 4) (dual of [(5, 4), 15, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(2⁵, 5, F₂, 3, 4) (dual of [(5, 3), 10, 5]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,10P) [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(2¹¹⁵, 4194301, F₂, 4, 8) (dual of [(4194301, 4), 16777089, 9]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(2¹¹⁵, 8388602, F₂, 2, 8) (dual of [(8388602, 2), 16777089, 9]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2¹¹⁵, large, F₂, 2, 8), 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.