MinT - Information on Result #941747

Information on Result #941747

Linear OOA(3¹⁰², 53, F₃, 2, 80) (dual of [(53, 2), 4, 81]-NRT-code), using juxtaposition based on

linear OOA(3¹⁰, 7, F₃, 2, 9) (dual of [(7, 2), 4, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,4P) [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(3⁸⁸, 46, F₃, 2, 70) (dual of [(46, 2), 4, 71]-NRT-code), using
- juxtaposition [i] based on
  1. 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 (see above)
  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(3¹⁰², 53, F₃, 2, 79) (dual of [(53, 2), 4, 80]-NRT-code)	[i]		Strength Reduction for OOAs