MinT - Information on Result #909211

Information on Result #909211

Linear OOA(3¹²⁵, 65, F₃, 2, 86) (dual of [(65, 2), 5, 87]-NRT-code), using juxtaposition based on

linear OOA(3³¹, 18, F₃, 2, 23) (dual of [(18, 2), 5, 24]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁸, 6, F₃, 2, 7) (dual of [(6, 2), 4, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁸, 7, F₃, 2, 7) (dual of [(7, 2), 6, 8]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,6P) [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(3¹¹, 6, F₃, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
    - dual of repetition NRT-code with length 6 [i]
  3. linear OOA(3¹², 6, F₃, 2, 12) (dual of [(6, 2), 0, 13]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
linear OOA(3⁸⁹, 47, F₃, 2, 62) (dual of [(47, 2), 5, 63]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3¹⁹, 12, F₃, 2, 15) (dual of [(12, 2), 5, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3⁶⁵, 35, F₃, 2, 46) (dual of [(35, 2), 5, 47]-NRT-code), using
    - 9 step truncation [i] based on linear OOA(3⁷⁴, 40, F₃, 2, 55) (dual of [(40, 2), 6, 56]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(9⁷, 10, F₉, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,9)), using
        extended Reedâ€“Solomon code RS_e(3,9) [i]
        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.