MinT - Information on Result #2776347

Information on Result #2776347

Linear OOA(3²³², 75, F₃, 4, 122) (dual of [(75, 4), 68, 123]-NRT-code), using strength reduction based on linear OOA(3²³², 75, F₃, 4, 123) (dual of [(75, 4), 68, 124]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁵⁶, 25, F₃, 4, 41) (dual of [(25, 4), 44, 42]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁵⁶, 28, F₃, 4, 41) (dual of [(28, 4), 56, 42]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,70P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
2. linear OOA(3⁷⁶, 25, F₃, 4, 61) (dual of [(25, 4), 24, 62]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁷⁶, 28, F₃, 4, 61) (dual of [(28, 4), 36, 62]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,50P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
3. linear OOA(3¹⁰⁰, 25, F₃, 4, 100) (dual of [(25, 4), 0, 101]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]

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.