MinT - Information on Result #909595

Information on Result #909595

Linear OOA(4¹⁶⁷, 87, F₄, 2, 121) (dual of [(87, 2), 7, 122]-NRT-code), using juxtaposition based on

linear OOA(4²⁷, 17, F₄, 2, 22) (dual of [(17, 2), 7, 23]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,11P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4¹³³, 70, F₄, 2, 98) (dual of [(70, 2), 7, 99]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4²¹, 14, F₄, 2, 18) (dual of [(14, 2), 7, 19]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,9P) [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(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 (see above)
      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.