MinT - Information on Result #2448088

Information on Result #2448088

Linear OOA(5¹³¹, 68, F₅, 2, 105) (dual of [(68, 2), 5, 106]-NRT-code), using strength reduction based on linear OOA(5¹³¹, 68, F₅, 2, 107) (dual of [(68, 2), 5, 108]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(5³¹, 18, F₅, 2, 27) (dual of [(18, 2), 5, 28]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₅ with g(F) = 4 and N(F) ≥ 18, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(5⁹⁵, 50, F₅, 2, 79) (dual of [(50, 2), 5, 80]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(5¹⁶, 10, F₅, 2, 15) (dual of [(10, 2), 4, 16]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(5¹⁹, 10, F₅, 2, 19) (dual of [(10, 2), 1, 20]-NRT-code), using
      - dual of repetition NRT-code with length 10 [i]
    3. linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code) (see above)
    5. linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-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.