MinT - Information on Result #2448555

Information on Result #2448555

Linear OOA(5¹⁴⁹, 77, F₅, 2, 119) (dual of [(77, 2), 5, 120]-NRT-code), using strength reduction based on linear OOA(5¹⁴⁹, 77, F₅, 2, 120) (dual of [(77, 2), 5, 121]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(5²⁵, 15, F₅, 2, 22) (dual of [(15, 2), 5, 23]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5²⁵, 16, F₅, 2, 22) (dual of [(16, 2), 7, 23]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,9P) [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(5¹¹⁹, 62, F₅, 2, 97) (dual of [(62, 2), 5, 98]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(5¹⁹, 12, F₅, 2, 17) (dual of [(12, 2), 5, 18]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₅ with g(F) = 2 and N(F) ≥ 12, 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
        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]
        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]
        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]
        linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code) (see above)
        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.