MinT - Information on Result #909130

Information on Result #909130

Linear OOA(3¹⁶⁶, 86, F₃, 2, 112) (dual of [(86, 2), 6, 113]-NRT-code), using juxtaposition based on

linear OOA(3²², 14, F₃, 2, 16) (dual of [(14, 2), 6, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,11P) [i] based on function field F/F₃ with g(F) = 6 and N(F) ≥ 14, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹³⁸, 72, F₃, 2, 95) (dual of [(72, 2), 6, 96]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(3⁶⁶, 36, F₃, 2, 47) (dual of [(36, 2), 6, 48]-NRT-code), using
  - generalized (u,Â u+v)-construction [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(3²³, 12, F₃, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
      - dual of repetition NRT-code with length 12 [i]
    3. linear OOA(3²⁴, 12, F₃, 2, 24) (dual of [(12, 2), 0, 25]-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(3¹⁹⁴, 100, F₃, 2, 129) (dual of [(100, 2), 6, 130]-NRT-code)	[i]		Juxtaposition for OOAs