MinT - Information on Result #2613880

Information on Result #2613880

Linear OOA(2¹⁶³, 56, F₂, 3, 114) (dual of [(56, 3), 5, 115]-NRT-code), using strength reduction based on linear OOA(2¹⁶³, 56, F₂, 3, 116) (dual of [(56, 3), 5, 117]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁴⁸, 51, F₂, 3, 106) (dual of [(51, 3), 5, 107]-NRT-code), using
  - strength reduction [i] based on linear OOA(2¹⁴⁸, 51, F₂, 3, 107) (dual of [(51, 3), 5, 108]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2¹³, 6, F₂, 3, 11) (dual of [(6, 3), 5, 12]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,6P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(2¹³⁰, 45, F₂, 3, 95) (dual of [(45, 3), 5, 96]-NRT-code), using
        2¹ times duplication [i] based on linear OOA(2¹²⁹, 45, F₂, 3, 95) (dual of [(45, 3), 6, 96]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
        extended Reedâ€“Solomon code RS_e(2,8) [i]
        Simplex code S(2,8) [i]
        linear OOA(2¹², 5, F₂, 3, 11) (dual of [(5, 3), 3, 12]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5 (see above)

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.