MinT - Information on Result #2447989

Information on Result #2447989

Linear OOA(5¹²⁷, 66, F₅, 2, 100) (dual of [(66, 2), 5, 101]-NRT-code), using strength reduction based on linear OOA(5¹²⁷, 66, F₅, 2, 102) (dual of [(66, 2), 5, 103]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(5⁷, 6, F₅, 2, 7) (dual of [(6, 2), 5, 8]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;5,5) [i]
2. linear OOA(5¹¹⁵, 60, F₅, 2, 94) (dual of [(60, 2), 5, 95]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(5²⁰, 12, F₅, 2, 18) (dual of [(12, 2), 4, 19]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,5P) [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(5²³, 12, F₅, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
      - dual of repetition NRT-code with length 12 [i]
    3. linear OOA(5²⁴, 12, F₅, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(5²⁴, 12, F₅, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code) (see above)
    5. linear OOA(5²⁴, 12, F₅, 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.