MinT - Information on Result #2806056

Information on Result #2806056

Linear OOA(3²⁴², 86, F₃, 4, 111) (dual of [(86, 4), 102, 112]-NRT-code), using 3² times duplication based on linear OOA(3²⁴⁰, 86, F₃, 4, 111) (dual of [(86, 4), 104, 112]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁵², 28, F₃, 4, 37) (dual of [(28, 4), 60, 38]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,74P) [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(3⁷⁰, 28, F₃, 4, 55) (dual of [(28, 4), 42, 56]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,56P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
3. linear OOA(3¹¹⁸, 30, F₃, 4, 111) (dual of [(30, 4), 2, 112]-NRT-code), using
  - 8 step truncation [i] based on linear OOA(3¹²⁶, 32, F₃, 4, 119) (dual of [(32, 4), 2, 120]-NRT-code), using
    - repeating each code word 8 times [i] based on linear OOA(3¹⁴, 4, F₃, 4, 14) (dual of [(4, 4), 2, 15]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(4;2,3) [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.