MinT - Information on Result #2439610

Information on Result #2439610

Linear OOA(4¹⁰⁹, 57, F₄, 2, 81) (dual of [(57, 2), 5, 82]-NRT-code), using strength reduction based on linear OOA(4¹⁰⁹, 57, F₄, 2, 84) (dual of [(57, 2), 5, 85]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
2. linear OOA(4⁹¹, 48, F₄, 2, 71) (dual of [(48, 2), 5, 72]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(4²⁰, 12, F₄, 2, 17) (dual of [(12, 2), 4, 18]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(4²⁰, 14, F₄, 2, 17) (dual of [(14, 2), 8, 18]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,10P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(4²³, 12, F₄, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
      - dual of repetition NRT-code with length 12 [i]
    3. linear OOA(4²⁴, 12, F₄, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(4²⁴, 12, F₄, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code) (see above)

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.