MinT - Information on Result #2805960

Information on Result #2805960

Linear OOA(3²²⁶, 81, F₃, 4, 105) (dual of [(81, 4), 98, 106]-NRT-code), using 3² times duplication based on linear OOA(3²²⁴, 81, F₃, 4, 105) (dual of [(81, 4), 100, 106]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁵⁰, 27, F₃, 4, 35) (dual of [(27, 4), 58, 36]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁵⁰, 28, F₃, 4, 35) (dual of [(28, 4), 62, 36]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,76P) [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, 105) (dual of [(27, 4), 1, 106]-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.