MinT - Information on Result #664032

Information on Result #664032

Linear OA(9¹¹⁵, 128, F₉, 79) (dual of [128, 13, 80]-code), using generalized (u,Â u+v)-construction based on

linear OA(9¹⁰, 16, F₉, 9) (dual of [16, 6, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹⁰, 20, F₉, 9) (dual of [20, 10, 10]-code), using
  - extended quadratic residue code Q_e(20,9) [i]
linear OA(9¹², 16, F₉, 11) (dual of [16, 4, 12]-code), using
- extended algebraic-geometric code AG_e(F,4P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
  - a function field by GarcÃa and Quoos [i]
linear OA(9¹⁴, 16, F₉, 13) (dual of [16, 2, 14]-code), using
- 4 times truncation [i] based on linear OA(9¹⁸, 20, F₉, 17) (dual of [20, 2, 18]-code), using
  - repeating each code word 2 times [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 OA(9¹⁵, 16, F₉, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,9)), using
- dual of repetition code with length 16 [i]
linear OA(9¹⁶, 16, F₉, 16) (dual of [16, 0, 17]-code or 16-arc in PG(15,9)), using
- complete OA / dual of code with only one code word [i]
linear OA(9¹⁶, 16, F₉, 16) (dual of [16, 0, 17]-code or 16-arc in PG(15,9)) (see above)
linear OA(9¹⁶, 16, F₉, 16) (dual of [16, 0, 17]-code or 16-arc in PG(15,9)) (see above)
linear OA(9¹⁶, 16, F₉, 16) (dual of [16, 0, 17]-code or 16-arc in PG(15,9)) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(9¹¹⁵, 64, F₉, 2, 79) (dual of [(64, 2), 13, 80]-NRT-code)	[i]		OOA Folding