MinT - Information on Result #941735

Information on Result #941735

Linear OOA(3⁹⁶, 50, F₃, 2, 75) (dual of [(50, 2), 4, 76]-NRT-code), using juxtaposition based on

linear OOA(3⁸, 6, F₃, 2, 7) (dual of [(6, 2), 4, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁸, 7, F₃, 2, 7) (dual of [(7, 2), 6, 8]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3⁸⁴, 44, F₃, 2, 67) (dual of [(44, 2), 4, 68]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;4,3) [i]
  2. linear OOA(3⁷⁶, 40, F₃, 2, 62) (dual of [(40, 2), 4, 63]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(9⁸, 10, F₉, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
        extended Reedâ€“Solomon code RS_e(2,9) [i]
        Simplex code S(2,9) [i]
      2. linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹¹⁰, 57, F₃, 2, 85) (dual of [(57, 2), 4, 86]-NRT-code)	[i]		Juxtaposition for OOAs
2	Linear OOA(3⁹⁶, 25, F₃, 4, 75) (dual of [(25, 4), 4, 76]-NRT-code)	[i]		OOA Folding