MinT - Information on Result #1049563

Information on Result #1049563

Linear OOA(3¹⁷³, 59, F₃, 3, 143) (dual of [(59, 3), 4, 144]-NRT-code), using juxtaposition based on

linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;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(3¹⁵², 52, F₃, 3, 126) (dual of [(52, 3), 4, 127]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3¹⁴, 6, F₃, 3, 13) (dual of [(6, 3), 4, 14]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3¹⁴, 7, F₃, 3, 13) (dual of [(7, 3), 7, 14]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7 (see above)
  2. linear OOA(3¹³⁴, 46, F₃, 3, 112) (dual of [(46, 3), 4, 113]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3¹⁴, 6, F₃, 3, 13) (dual of [(6, 3), 4, 14]-NRT-code) (see above)
      2. linear OOA(3¹¹⁶, 40, F₃, 3, 98) (dual of [(40, 3), 4, 99]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        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]
        linear OOA(3¹⁰, 4, F₃, 3, 10) (dual of [(4, 3), 2, 11]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;2,3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁹⁴, 66, F₃, 3, 160) (dual of [(66, 3), 4, 161]-NRT-code)	[i]		Juxtaposition for OOAs