MinT - Information on Result #2470475

Information on Result #2470475

Linear OOA(4²³¹, 118, F₄, 2, 180) (dual of [(118, 2), 5, 181]-NRT-code), using 15 step truncation based on linear OOA(4²⁴⁶, 126, F₄, 2, 195) (dual of [(126, 2), 6, 196]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁶⁶, 36, F₄, 2, 51) (dual of [(36, 2), 6, 52]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
    2. linear OOA(4¹⁷, 9, F₄, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
      - dual of repetition NRT-code with length 9 [i]
    3. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)
2. linear OOA(4¹⁷⁴, 90, F₄, 2, 143) (dual of [(90, 2), 6, 144]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(16¹⁵, 18, F₁₆, 15) (dual of [18, 3, 16]-code or 18-arc in PG(14,16)), using
      - Denniston code D(1,16) [i]
    2. linear OOA(4⁸, 5, F₄, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,4) [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.