MinT - Information on Result #1080524

Information on Result #1080524

Linear OOA(2²²⁷, 70, F₂, 4, 91) (dual of [(70, 4), 53, 92]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁸⁴, 33, F₂, 4, 45) (dual of [(33, 4), 48, 46]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,86P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁴³, 37, F₂, 4, 91) (dual of [(37, 4), 5, 92]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁴³, 74, F₂, 2, 91) (dual of [(74, 2), 5, 92]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2¹⁷, 11, F₂, 2, 11) (dual of [(11, 2), 5, 12]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
        linear OOA(2¹¹, 6, F₂, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
        dual of repetition NRT-code with length 6 [i]
    2. linear OOA(2¹²¹, 63, F₂, 2, 79) (dual of [(63, 2), 5, 80]-NRT-code), using
      - 2¹ times duplication [i] based on linear OOA(2¹²⁰, 63, F₂, 2, 79) (dual of [(63, 2), 6, 80]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(4¹⁸, 21, F₄, 15) (dual of [21, 3, 16]-code), using
        Simplex code S(3,4) [i]
        linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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.