MinT - Information on Result #2439710

Information on Result #2439710

Linear OOA(4¹¹³, 60, F₄, 2, 81) (dual of [(60, 2), 7, 82]-NRT-code), using strength reduction based on linear OOA(4¹¹³, 60, F₄, 2, 83) (dual of [(60, 2), 7, 84]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(4²⁴, 15, F₄, 2, 20) (dual of [(15, 2), 6, 21]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(4²⁹, 15, F₄, 2, 27) (dual of [(15, 2), 1, 28]-NRT-code), using
  - strength reduction [i] based on linear OOA(4²⁹, 15, F₄, 2, 29) (dual of [(15, 2), 1, 30]-NRT-code), using
    - dual of repetition NRT-code with length 15 [i]
3. linear OOA(4³⁰, 15, F₄, 2, 30) (dual of [(15, 2), 0, 31]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
4. linear OOA(4³⁰, 15, F₄, 2, 30) (dual of [(15, 2), 0, 31]-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.