MinT - Information on Result #1167573

Information on Result #1167573

Linear OOA(2⁶¹, 8, F₂, 8, 51) (dual of [(8, 8), 3, 52]-NRT-code), using OOA 2-folding based on linear OOA(2⁶¹, 16, F₂, 4, 51) (dual of [(16, 4), 3, 52]-NRT-code), using

strength reduction [i] based on linear OOA(2⁶¹, 16, F₂, 4, 53) (dual of [(16, 4), 3, 54]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2⁹, 3, F₂, 4, 9) (dual of [(3, 4), 3, 10]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(4;3,2) [i]
  2. linear OOA(2⁴⁹, 13, F₂, 4, 43) (dual of [(13, 4), 3, 44]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2⁹, 3, F₂, 4, 9) (dual of [(3, 4), 3, 10]-NRT-code) (see above)
      2. linear OOA(2³⁷, 10, F₂, 4, 33) (dual of [(10, 4), 3, 34]-NRT-code), using
        repeating each code word 2 times [i] based on linear OOA(2¹⁷, 5, F₂, 4, 16) (dual of [(5, 4), 3, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.