MinT - Information on Result #1025224

Information on Result #1025224

Linear OOA(2¹⁸⁷, 66, F₂, 3, 100) (dual of [(66, 3), 11, 101]-NRT-code), using juxtaposition based on

linear OOA(2⁴⁰, 17, F₂, 3, 25) (dual of [(17, 3), 11, 26]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,25P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹³⁶, 49, F₂, 3, 74) (dual of [(49, 3), 11, 75]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2³¹, 14, F₂, 3, 20) (dual of [(14, 3), 11, 21]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,21P) [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁹⁴, 35, F₂, 3, 53) (dual of [(35, 3), 11, 54]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁴¹, 17, F₂, 3, 26) (dual of [(17, 3), 10, 27]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,24P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17 (see above)
      2. linear OOA(2⁵³, 18, F₂, 3, 53) (dual of [(18, 3), 1, 54]-NRT-code), using
        dual of repetition NRT-code with length 18 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²³⁸, 83, F₂, 3, 126) (dual of [(83, 3), 11, 127]-NRT-code)	[i]		Juxtaposition for OOAs