MinT - Information on Result #2253323

Information on Result #2253323

Linear OA(9¹²⁹, 141, F₉, 92) (dual of [141, 12, 93]-code), using 3 times truncation based on linear OA(9¹³², 144, F₉, 95) (dual of [144, 12, 96]-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OA(9¹¹, 16, F₉, 10) (dual of [16, 5, 11]-code), using
  - extended algebraic-geometric code AG_e(F,5P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
    - a function field by GarcÃa and Quoos [i]
2. 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 (see above)
3. 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]
4. 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]
5. 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]
6. linear OA(9¹⁶, 16, F₉, 16) (dual of [16, 0, 17]-code or 16-arc in PG(15,9)) (see above)
7. linear OA(9¹⁶, 16, F₉, 16) (dual of [16, 0, 17]-code or 16-arc in PG(15,9)) (see above)
8. linear OA(9¹⁶, 16, F₉, 16) (dual of [16, 0, 17]-code or 16-arc in PG(15,9)) (see above)
9. 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(9¹²⁹, 47, F₉, 3, 92) (dual of [(47, 3), 12, 93]-NRT-code)	[i]		OOA Folding