MinT - Information on Result #909816

Information on Result #909816

Linear OOA(4²⁵⁴, 129, F₄, 2, 200) (dual of [(129, 2), 4, 201]-NRT-code), using juxtaposition based on

linear OOA(4⁴, 4, F₄, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
- Reedâ€“Solomon NRT-code RS(2;4,4) [i]
linear OOA(4²⁴⁶, 125, F₄, 2, 195) (dual of [(125, 2), 4, 196]-NRT-code), using
- discarding factors / shortening the dual code 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
        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]
        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]
        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]
        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
        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]
        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.