MinT - Information on Result #909192

Information on Result #909192

Linear OOA(3¹¹⁹, 62, F₃, 2, 82) (dual of [(62, 2), 5, 83]-NRT-code), using juxtaposition based on

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]
linear OOA(3⁹⁵, 50, F₃, 2, 66) (dual of [(50, 2), 5, 67]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3¹⁹, 12, F₃, 2, 15) (dual of [(12, 2), 5, 16]-NRT-code) (see above)
  2. linear OOA(3⁷¹, 38, F₃, 2, 50) (dual of [(38, 2), 5, 51]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(3²⁰, 12, F₃, 2, 16) (dual of [(12, 2), 4, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12 (see above)
      2. linear OOA(3²⁵, 13, F₃, 2, 25) (dual of [(13, 2), 1, 26]-NRT-code), using
        dual of repetition NRT-code with length 13 [i]
      3. linear OOA(3²⁶, 13, F₃, 2, 26) (dual of [(13, 2), 0, 27]-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(3¹⁴³, 74, F₃, 2, 98) (dual of [(74, 2), 5, 99]-NRT-code)	[i]		Juxtaposition for OOAs