MinT - Information on Result #2627510

Information on Result #2627510

Linear OOA(3²²⁴, 81, F₃, 3, 144) (dual of [(81, 3), 19, 145]-NRT-code), using strength reduction based on linear OOA(3²²⁴, 81, F₃, 3, 147) (dual of [(81, 3), 19, 148]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁶⁴, 27, F₃, 3, 49) (dual of [(27, 3), 17, 50]-NRT-code), using
  - algebraic-geometric NRT-code AG(3;F,31P) [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(3⁷⁹, 27, F₃, 3, 73) (dual of [(27, 3), 2, 74]-NRT-code), using
  - 3 step truncation [i] based on linear OOA(3⁸², 28, F₃, 3, 76) (dual of [(28, 3), 2, 77]-NRT-code), using
    - repeating each code word 7 times [i] based on linear OOA(3¹⁰, 4, F₃, 3, 10) (dual of [(4, 3), 2, 11]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;2,3) [i]
3. linear OOA(3⁸¹, 27, F₃, 3, 81) (dual of [(27, 3), 0, 82]-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.