MinT - Information on Result #2777501

Information on Result #2777501

Linear OOA(3²⁴⁷, 87, F₃, 4, 112) (dual of [(87, 4), 101, 113]-NRT-code), using strength reduction based on linear OOA(3²⁴⁷, 87, F₃, 4, 115) (dual of [(87, 4), 101, 116]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3⁵³, 28, F₃, 4, 38) (dual of [(28, 4), 59, 39]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,73P) [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(3⁷², 28, F₃, 4, 57) (dual of [(28, 4), 40, 58]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,54P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
3. linear OOA(3¹²², 31, F₃, 4, 115) (dual of [(31, 4), 2, 116]-NRT-code), using
  - 4 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.