MinT - Information on Result #2474816

Information on Result #2474816

Linear OOA(5¹³⁹, 72, F₅, 2, 112) (dual of [(72, 2), 5, 113]-NRT-code), using 6 step truncation based on linear OOA(5¹⁴⁵, 75, F₅, 2, 118) (dual of [(75, 2), 5, 119]-NRT-code), using

strength reduction [i] based on linear OOA(5¹⁴⁵, 75, F₅, 2, 119) (dual of [(75, 2), 5, 120]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(5²⁶, 15, F₅, 2, 23) (dual of [(15, 2), 4, 24]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5²⁶, 16, F₅, 2, 23) (dual of [(16, 2), 6, 24]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₅ with g(F) = 3 and N(F) ≥ 16, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(5²⁹, 15, F₅, 2, 29) (dual of [(15, 2), 1, 30]-NRT-code), using
    - dual of repetition NRT-code with length 15 [i]
  3. linear OOA(5³⁰, 15, F₅, 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(5³⁰, 15, F₅, 2, 30) (dual of [(15, 2), 0, 31]-NRT-code) (see above)
  5. linear OOA(5³⁰, 15, F₅, 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.