MinT - Information on Result #2419455

Information on Result #2419455

Linear OOA(2¹²⁶, 65, F₂, 2, 84) (dual of [(65, 2), 4, 85]-NRT-code), using strength reduction based on linear OOA(2¹²⁶, 65, F₂, 2, 85) (dual of [(65, 2), 4, 86]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,4P) [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(2¹¹⁶, 60, F₂, 2, 79) (dual of [(60, 2), 4, 80]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(4¹⁸, 20, F₄, 15) (dual of [20, 2, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁸, 21, F₄, 15) (dual of [21, 3, 16]-code), using
        Simplex code S(3,4) [i]
    2. linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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.