MinT - Information on Result #2436400

Information on Result #2436400

Linear OOA(3²²³, 114, F₃, 2, 167) (dual of [(114, 2), 5, 168]-NRT-code), using strength reduction based on linear OOA(3²²³, 114, F₃, 2, 168) (dual of [(114, 2), 5, 169]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁹, 7, F₃, 2, 8) (dual of [(7, 2), 5, 9]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3²⁰⁹, 107, F₃, 2, 159) (dual of [(107, 2), 5, 160]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(3²¹⁰, 108, F₃, 2, 160) (dual of [(108, 2), 6, 161]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(9²⁴, 27, F₉, 22) (dual of [27, 3, 23]-code), using
        algebraic-geometric code AG(F,4P) with known gap numbers [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using the Hermitian function field over F₉ [i]
      2. linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [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.