MinT - Information on Result #909680

Information on Result #909680

Linear OOA(4¹⁷², 89, F₄, 2, 129) (dual of [(89, 2), 6, 130]-NRT-code), using juxtaposition based on

linear OOA(4²⁸, 17, F₄, 2, 23) (dual of [(17, 2), 6, 24]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,10P) [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(4¹³⁸, 72, F₄, 2, 105) (dual of [(72, 2), 6, 106]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4²⁶, 16, F₄, 2, 21) (dual of [(16, 2), 6, 22]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4²⁶, 17, F₄, 2, 21) (dual of [(17, 2), 8, 22]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,12P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17 (see above)
  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, using
        an explicitly constructive algebraic function field [i]
      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.