MinT - Information on Result #2444122

Information on Result #2444122

Linear OOA(4²²², 113, F₄, 2, 182) (dual of [(113, 2), 4, 183]-NRT-code), using strength reduction based on linear OOA(4²²², 113, F₄, 2, 186) (dual of [(113, 2), 4, 187]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4¹⁶, 10, F₄, 2, 14) (dual of [(10, 2), 4, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(4²⁰², 103, F₄, 2, 171) (dual of [(103, 2), 4, 172]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4¹⁴, 9, F₄, 2, 13) (dual of [(9, 2), 4, 14]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,4P) [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(4¹⁸⁴, 94, F₄, 2, 157) (dual of [(94, 2), 4, 158]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(4¹⁴, 9, F₄, 2, 13) (dual of [(9, 2), 4, 14]-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.