MinT - Information on Result #941799

Information on Result #941799

Linear OOA(3⁸⁷, 45, F₃, 2, 70) (dual of [(45, 2), 3, 71]-NRT-code), using juxtaposition based on

linear OOA(3⁹, 6, F₃, 2, 8) (dual of [(6, 2), 3, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁹, 7, F₃, 2, 8) (dual of [(7, 2), 5, 9]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,5P) [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(3⁷⁵, 39, F₃, 2, 61) (dual of [(39, 2), 3, 62]-NRT-code), using
- 1 step truncation [i] based on 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(3¹⁰¹, 52, F₃, 2, 81) (dual of [(52, 2), 3, 82]-NRT-code)	[i]		Juxtaposition for OOAs