MinT - Information on Result #909162

Information on Result #909162

Linear OOA(3⁵⁷, 31, F₃, 2, 40) (dual of [(31, 2), 5, 41]-NRT-code), using juxtaposition based on

linear OOA(3⁹, 7, F₃, 2, 8) (dual of [(7, 2), 5, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,5P) [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(3⁴³, 24, F₃, 2, 31) (dual of [(24, 2), 5, 32]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹², 8, F₃, 2, 10) (dual of [(8, 2), 4, 11]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3¹⁵, 8, F₃, 2, 15) (dual of [(8, 2), 1, 16]-NRT-code), using
    - dual of repetition NRT-code with length 8 [i]
  3. linear OOA(3¹⁶, 8, F₃, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3⁵⁷, 31, F₃, 2, 39) (dual of [(31, 2), 5, 40]-NRT-code)	[i]		Strength Reduction for OOAs