MinT - Information on Result #1049468

Information on Result #1049468

Linear OOA(2¹⁶⁹, 58, F₂, 3, 120) (dual of [(58, 3), 5, 121]-NRT-code), using juxtaposition based on

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]
linear OOA(2¹⁵⁴, 53, F₂, 3, 110) (dual of [(53, 3), 5, 111]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹⁵⁴, 53, F₂, 3, 111) (dual of [(53, 3), 5, 112]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2¹⁹, 8, F₂, 3, 15) (dual of [(8, 3), 5, 16]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,8P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, 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.

None.

The following results depend on this result: