MinT - Information on Result #2775670

Information on Result #2775670

Linear OOA(3²²³, 81, F₃, 4, 103) (dual of [(81, 4), 101, 104]-NRT-code), using strength reduction based on linear OOA(3²²³, 81, F₃, 4, 104) (dual of [(81, 4), 101, 105]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁴⁹, 27, F₃, 4, 34) (dual of [(27, 4), 59, 35]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁴⁹, 28, F₃, 4, 34) (dual of [(28, 4), 63, 35]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,77P) [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(3⁶⁷, 27, F₃, 4, 52) (dual of [(27, 4), 41, 53]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁶⁷, 28, F₃, 4, 52) (dual of [(28, 4), 45, 53]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,59P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
3. linear OOA(3¹⁰⁷, 27, F₃, 4, 104) (dual of [(27, 4), 1, 105]-NRT-code), using
  - strength reduction [i] based on linear OOA(3¹⁰⁷, 27, F₃, 4, 107) (dual of [(27, 4), 1, 108]-NRT-code), using
    - dual of repetition NRT-code with length 27 [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.