MinT - Information on Result #1025455

Information on Result #1025455

Linear OOA(2¹⁵¹, 53, F₂, 3, 88) (dual of [(53, 3), 8, 89]-NRT-code), using juxtaposition based on

linear OOA(2¹⁹, 9, F₂, 3, 14) (dual of [(9, 3), 8, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,12P) [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(2¹²⁴, 44, F₂, 3, 73) (dual of [(44, 3), 8, 74]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁶, 8, F₂, 3, 12) (dual of [(8, 3), 8, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,11P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹⁰⁰, 36, F₂, 3, 60) (dual of [(36, 3), 8, 61]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2¹⁶, 8, F₂, 3, 12) (dual of [(8, 3), 8, 13]-NRT-code) (see above)
      2. linear OOA(2⁷⁶, 28, F₂, 3, 47) (dual of [(28, 3), 8, 48]-NRT-code), using
        repeating each code word 2 times [i] based on linear OOA(2³⁴, 14, F₂, 3, 23) (dual of [(14, 3), 8, 24]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,18P) [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(2¹⁷⁸, 62, F₂, 3, 103) (dual of [(62, 3), 8, 104]-NRT-code)	[i]		Juxtaposition for OOAs