MinT - Information on Result #2806067

Information on Result #2806067

Linear OOA(3²⁴⁶, 87, F₃, 4, 112) (dual of [(87, 4), 102, 113]-NRT-code), using 3¹ times duplication based on linear OOA(3²⁴⁵, 87, F₃, 4, 112) (dual of [(87, 4), 103, 113]-NRT-code), using

strength reduction [i] based on linear OOA(3²⁴⁵, 87, F₃, 4, 113) (dual of [(87, 4), 103, 114]-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(3⁷¹, 28, F₃, 4, 56) (dual of [(28, 4), 41, 57]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,55P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
  3. linear OOA(3¹²², 31, F₃, 4, 113) (dual of [(31, 4), 2, 114]-NRT-code), using
    - 36 step truncation [i] based on linear OOA(3¹⁵⁸, 40, F₃, 4, 149) (dual of [(40, 4), 2, 150]-NRT-code), using
      - repeating each code word 10 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.