MinT - Information on Result #1025365

Information on Result #1025365

Linear OOA(2¹⁷⁷, 62, F₂, 3, 100) (dual of [(62, 3), 9, 101]-NRT-code), using juxtaposition based on

linear OOA(2²¹, 10, F₂, 3, 15) (dual of [(10, 3), 9, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,14P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁴⁷, 52, F₂, 3, 84) (dual of [(52, 3), 9, 85]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2²¹, 10, F₂, 3, 15) (dual of [(10, 3), 9, 16]-NRT-code) (see above)
  2. linear OOA(2¹¹⁷, 42, F₂, 3, 68) (dual of [(42, 3), 9, 69]-NRT-code), using
    - repeating each code word 3 times [i] based on linear OOA(2³³, 14, F₂, 3, 22) (dual of [(14, 3), 9, 23]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,19P) [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, 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(2²⁰⁷, 72, F₂, 3, 116) (dual of [(72, 3), 9, 117]-NRT-code)	[i]		Juxtaposition for OOAs