MinT - Information on Result #909647

Information on Result #909647

Linear OOA(4¹⁵⁰, 78, F₄, 2, 113) (dual of [(78, 2), 6, 114]-NRT-code), using juxtaposition based on

linear OOA(4²⁰, 13, F₄, 2, 17) (dual of [(13, 2), 6, 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]
linear OOA(4¹²⁴, 65, F₄, 2, 95) (dual of [(65, 2), 6, 96]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4¹², 9, F₄, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,6P) [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(4¹⁰⁶, 56, F₄, 2, 83) (dual of [(56, 2), 6, 84]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14 (see above)
      2. linear OOA(4²⁷, 14, F₄, 2, 27) (dual of [(14, 2), 1, 28]-NRT-code), using
        dual of repetition NRT-code with length 14 [i]
      3. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code), using
        complete OOA / dual of NRT-code with only one code word [i]
      4. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-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.