MinT - Information on Result #1025345

Information on Result #1025345

Linear OOA(2²²⁵, 78, F₂, 3, 126) (dual of [(78, 3), 9, 127]-NRT-code), using juxtaposition based on

linear OOA(2¹⁸, 9, F₂, 3, 13) (dual of [(9, 3), 9, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁹⁸, 69, F₂, 3, 112) (dual of [(69, 3), 9, 113]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁸, 9, F₂, 3, 13) (dual of [(9, 3), 9, 14]-NRT-code) (see above)
  2. linear OOA(2¹⁷¹, 60, F₂, 3, 98) (dual of [(60, 3), 9, 99]-NRT-code), using
    - repeating each code word 3 times [i] based on linear OOA(2⁵¹, 20, F₂, 3, 32) (dual of [(20, 3), 9, 33]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,27P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁵², 87, F₂, 3, 140) (dual of [(87, 3), 9, 141]-NRT-code)	[i]		Juxtaposition for OOAs