MinT - Information on Result #909768

Information on Result #909768

Linear OOA(4¹⁷⁵, 90, F₄, 2, 134) (dual of [(90, 2), 5, 135]-NRT-code), using juxtaposition based on

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]
linear OOA(4¹⁴⁷, 76, F₄, 2, 113) (dual of [(76, 2), 5, 114]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code) (see above)
  2. linear OOA(4¹¹⁹, 62, F₄, 2, 92) (dual of [(62, 2), 5, 93]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code) (see above)
      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
        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 (see above)
        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]
        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]
        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.