MinT - Information on Result #1049582

Information on Result #1049582

Linear OOA(3²⁰⁹, 71, F₃, 3, 173) (dual of [(71, 3), 4, 174]-NRT-code), using juxtaposition based on

linear OOA(3²⁶, 10, F₃, 3, 23) (dual of [(10, 3), 4, 24]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,6P) [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁷⁹, 61, F₃, 3, 149) (dual of [(61, 3), 4, 150]-NRT-code), using
- juxtaposition [i] based on
  1. 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]
  2. linear OOA(3¹⁵⁸, 54, F₃, 3, 132) (dual of [(54, 3), 4, 133]-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(3¹³⁷, 47, F₃, 3, 115) (dual of [(47, 3), 4, 116]-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(3¹¹⁶, 40, F₃, 3, 98) (dual of [(40, 3), 4, 99]-NRT-code), using
        concatenation of two NRT-codes [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 OOA(3¹⁰, 4, F₃, 3, 10) (dual of [(4, 3), 2, 11]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;2,3) [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, 172) (dual of [(71, 3), 4, 173]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²⁰⁴, 69, F₃, 3, 168) (dual of [(69, 3), 3, 169]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3¹⁹⁹, 67, F₃, 3, 163) (dual of [(67, 3), 2, 164]-NRT-code)	[i]
4	Linear OOA(3¹⁹³, 65, F₃, 3, 157) (dual of [(65, 3), 2, 158]-NRT-code)	[i]
5	Linear OOA(3¹⁸³, 62, F₃, 3, 147) (dual of [(62, 3), 3, 148]-NRT-code)	[i]
6	Linear OOA(3¹⁸¹, 61, F₃, 3, 145) (dual of [(61, 3), 2, 146]-NRT-code)	[i]
7	Linear OOA(3¹⁸⁰, 61, F₃, 3, 144) (dual of [(61, 3), 3, 145]-NRT-code)	[i]