MinT - Information on Result #2443889

Information on Result #2443889

Linear OOA(4²¹⁸, 111, F₄, 2, 180) (dual of [(111, 2), 4, 181]-NRT-code), using strength reduction based on linear OOA(4²¹⁸, 111, F₄, 2, 181) (dual of [(111, 2), 4, 182]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4¹², 8, F₄, 2, 11) (dual of [(8, 2), 4, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹², 9, F₄, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,6P) [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(4²⁰², 103, F₄, 2, 169) (dual of [(103, 2), 4, 170]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4¹², 8, F₄, 2, 11) (dual of [(8, 2), 4, 12]-NRT-code) (see above)
    2. linear OOA(4¹⁸⁶, 95, F₄, 2, 157) (dual of [(95, 2), 4, 158]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(4⁶, 5, F₄, 2, 6) (dual of [(5, 2), 4, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;4,4) [i]
        linear OOA(4¹⁷⁶, 90, F₄, 2, 150) (dual of [(90, 2), 4, 151]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(4⁶, 5, F₄, 2, 6) (dual of [(5, 2), 4, 7]-NRT-code) (see above)
        linear OOA(4¹⁶⁶, 85, F₄, 2, 143) (dual of [(85, 2), 4, 144]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(16¹⁵, 17, F₁₆, 15) (dual of [17, 2, 16]-code or 17-arc in PG(14,16)), using
        extended Reedâ€“Solomon code RS_e(2,16) [i]
        Simplex code S(2,16) [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.