MinT - Information on Result #1026582

Information on Result #1026582

Linear OOA(3²⁰⁹, 71, F₃, 3, 171) (dual of [(71, 3), 4, 172]-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(3¹⁸⁸, 64, F₃, 3, 154) (dual of [(64, 3), 4, 155]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code) (see above)
  2. linear OOA(3¹⁶⁷, 57, F₃, 3, 137) (dual of [(57, 3), 4, 138]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code) (see above)
      2. linear OOA(3¹⁴⁶, 50, F₃, 3, 120) (dual of [(50, 3), 4, 121]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code) (see above)
        linear OOA(3¹²⁵, 43, F₃, 3, 103) (dual of [(43, 3), 4, 104]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code) (see above)
        linear OOA(3¹⁰⁴, 36, F₃, 3, 86) (dual of [(36, 3), 4, 87]-NRT-code), using
        repeating each code word 3 times [i] based on linear OOA(3³², 12, F₃, 3, 28) (dual of [(12, 3), 4, 29]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
        an explicitly constructive algebraic function field [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		Method
1	Linear OOA(3²⁰⁹, 71, F₃, 3, 170) (dual of [(71, 3), 4, 171]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²⁰⁹, 71, F₃, 3, 169) (dual of [(71, 3), 4, 170]-NRT-code)	[i]
3	Linear OOA(3²⁰⁹, 71, F₃, 3, 168) (dual of [(71, 3), 4, 169]-NRT-code)	[i]
4	Linear OOA(3²⁰⁹, 71, F₃, 3, 167) (dual of [(71, 3), 4, 168]-NRT-code)	[i]
5	Linear OOA(3²⁰⁹, 71, F₃, 3, 166) (dual of [(71, 3), 4, 167]-NRT-code)	[i]
6	Linear OOA(3²⁰⁹, 71, F₃, 3, 165) (dual of [(71, 3), 4, 166]-NRT-code)	[i]
7	Linear OOA(3²⁰⁹, 71, F₃, 3, 164) (dual of [(71, 3), 4, 165]-NRT-code)	[i]
8	Linear OOA(3²⁰⁹, 71, F₃, 3, 163) (dual of [(71, 3), 4, 164]-NRT-code)	[i]
9	Linear OOA(3²⁰⁹, 71, F₃, 3, 162) (dual of [(71, 3), 4, 163]-NRT-code)	[i]
10	Linear OOA(3²⁰⁹, 71, F₃, 3, 161) (dual of [(71, 3), 4, 162]-NRT-code)	[i]
11	Linear OOA(3²³⁰, 78, F₃, 3, 188) (dual of [(78, 3), 4, 189]-NRT-code)	[i]	Juxtaposition for OOAs