MinT - Information on Result #2627883

Information on Result #2627883

Linear OOA(3²³⁰, 79, F₃, 3, 170) (dual of [(79, 3), 7, 171]-NRT-code), using strength reduction based on linear OOA(3²³⁰, 79, F₃, 3, 174) (dual of [(79, 3), 7, 175]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3²⁹, 12, F₃, 3, 25) (dual of [(12, 3), 7, 26]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,10P) [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(3¹⁹⁴, 67, F₃, 3, 148) (dual of [(67, 3), 7, 149]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3²⁶, 11, F₃, 3, 22) (dual of [(11, 3), 7, 23]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3²⁶, 12, F₃, 3, 22) (dual of [(12, 3), 10, 23]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12 (see above)
    2. linear OOA(3¹⁶¹, 56, F₃, 3, 125) (dual of [(56, 3), 7, 126]-NRT-code), using
      - repeating each code word 2 times [i] based on linear OOA(3⁷⁷, 28, F₃, 3, 62) (dual of [(28, 3), 7, 63]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,21P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, 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.