MinT - Information on Result #988164

Information on Result #988164

Linear OOA(9¹³², 48, F₉, 3, 93) (dual of [(48, 3), 12, 94]-NRT-code), using OOA 3-folding based on linear OA(9¹³², 144, F₉, 93) (dual of [144, 12, 94]-code), using

strength reduction [i] 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

None.