MinT - Information on Result #2439952

Information on Result #2439952

Linear OOA(4¹²³, 65, F₄, 2, 89) (dual of [(65, 2), 7, 90]-NRT-code), using strength reduction based on linear OOA(4¹²³, 65, F₄, 2, 90) (dual of [(65, 2), 7, 91]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4¹¹, 9, F₄, 2, 10) (dual of [(9, 2), 7, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,7P) [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(4¹⁰⁵, 56, F₄, 2, 79) (dual of [(56, 2), 7, 80]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(4²², 14, F₄, 2, 19) (dual of [(14, 2), 6, 20]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,8P) [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(4²⁷, 14, F₄, 2, 26) (dual of [(14, 2), 1, 27]-NRT-code), using
      - strength reduction [i] based on 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.