MinT - Information on Result #2622684

Information on Result #2622684

Linear OOA(3¹³⁷, 47, F₃, 3, 112) (dual of [(47, 3), 4, 113]-NRT-code), using strength reduction based on linear OOA(3¹³⁷, 47, F₃, 3, 113) (dual of [(47, 3), 4, 114]-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(3¹¹⁶, 40, F₃, 3, 96) (dual of [(40, 3), 4, 97]-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(3⁹⁵, 33, F₃, 3, 79) (dual of [(33, 3), 4, 80]-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(3⁷⁴, 26, F₃, 3, 62) (dual of [(26, 3), 4, 63]-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(3⁵³, 19, F₃, 3, 45) (dual of [(19, 3), 4, 46]-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(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		This result only	Method
1	Linear OOA(3²³⁸, 92, F₃, 3, 112) (dual of [(92, 3), 38, 113]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁴⁹, 51, F₃, 3, 121) (dual of [(51, 3), 4, 122]-NRT-code)	[i]		Juxtaposition for OOAs