MinT - Information on Result #2782531

Information on Result #2782531

Linear OOA(2²⁵⁷, 67, F₂, 4, 174) (dual of [(67, 4), 11, 175]-NRT-code), using 3 step truncation based on linear OOA(2²⁶⁰, 68, F₂, 4, 177) (dual of [(68, 4), 12, 178]-NRT-code), using

strength reduction [i] based on linear OOA(2²⁶⁰, 68, F₂, 4, 179) (dual of [(68, 4), 12, 180]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16¹⁴, 17, F₁₆, 14) (dual of [17, 3, 15]-code or 17-arc in PG(13,16)), using
    - extended Reedâ€“Solomon code RS_e(3,16) [i]
  2. linear OOA(2¹², 4, F₂, 4, 11) (dual of [(4, 4), 4, 12]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2¹², 5, F₂, 4, 11) (dual of [(5, 4), 8, 12]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,8P) [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.