MinT - Information on Result #909219

Information on Result #909219

Linear OOA(3¹⁶⁵, 85, F₃, 2, 113) (dual of [(85, 2), 5, 114]-NRT-code), using juxtaposition based on

linear OOA(3⁶⁵, 35, F₃, 2, 46) (dual of [(35, 2), 5, 47]-NRT-code), using
- 9 step truncation [i] based on linear OOA(3⁷⁴, 40, F₃, 2, 55) (dual of [(40, 2), 6, 56]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(9⁷, 10, F₉, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,9)), using
      - extended Reedâ€“Solomon code RS_e(3,9) [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]
linear OOA(3⁹⁵, 50, F₃, 2, 66) (dual of [(50, 2), 5, 67]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3¹⁹, 12, F₃, 2, 15) (dual of [(12, 2), 5, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3⁷¹, 38, F₃, 2, 50) (dual of [(38, 2), 5, 51]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(3²⁰, 12, F₃, 2, 16) (dual of [(12, 2), 4, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12 (see above)
      2. linear OOA(3²⁵, 13, F₃, 2, 25) (dual of [(13, 2), 1, 26]-NRT-code), using
        dual of repetition NRT-code with length 13 [i]
      3. linear OOA(3²⁶, 13, F₃, 2, 26) (dual of [(13, 2), 0, 27]-NRT-code), using
        complete OOA / dual of NRT-code with only one code word [i]

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(3²³⁵, 120, F₃, 2, 160) (dual of [(120, 2), 5, 161]-NRT-code)	[i]		Juxtaposition for OOAs