MinT - Information on Result #2781639

Information on Result #2781639

Linear OOA(2²⁰⁹, 54, F₂, 4, 155) (dual of [(54, 4), 7, 156]-NRT-code), using 3 step truncation based on linear OOA(2²¹², 55, F₂, 4, 158) (dual of [(55, 4), 8, 159]-NRT-code), using

strength reduction [i] based on linear OOA(2²¹², 55, F₂, 4, 159) (dual of [(55, 4), 8, 160]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16⁹, 11, F₁₆, 9) (dual of [11, 2, 10]-code or 11-arc in PG(8,16)), using
    - discarding factors / shortening the dual code based on linear OA(16⁹, 16, F₁₆, 9) (dual of [16, 7, 10]-code or 16-arc in PG(8,16)), using
      - Reedâ€“Solomon code RS(7,16) [i]
  2. linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;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]

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.