MinT - Information on Result #909149

Information on Result #909149

Linear OOA(3¹²⁴, 65, F₃, 2, 84) (dual of [(65, 2), 6, 85]-NRT-code), using juxtaposition based on

linear OOA(3⁵², 29, F₃, 2, 36) (dual of [(29, 2), 6, 37]-NRT-code), using
- 2 step truncation [i] based on linear OOA(3⁵⁴, 30, F₃, 2, 38) (dual of [(30, 2), 6, 39]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3¹⁵, 10, F₃, 2, 12) (dual of [(10, 2), 5, 13]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(3¹⁹, 10, F₃, 2, 19) (dual of [(10, 2), 1, 20]-NRT-code), using
      - dual of repetition NRT-code with length 10 [i]
    3. linear OOA(3²⁰, 10, F₃, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
linear OOA(3⁶⁶, 36, F₃, 2, 47) (dual of [(36, 2), 6, 48]-NRT-code), using
- generalized (u,Â u+v)-construction [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(3²³, 12, F₃, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
    - dual of repetition NRT-code with length 12 [i]
  3. linear OOA(3²⁴, 12, F₃, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [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.