MinT - Information on Result #894628

Information on Result #894628

Linear OOA(2⁸⁵, 46, F₂, 2, 45) (dual of [(46, 2), 7, 46]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁰, 23, F₂, 2, 22) (dual of [(23, 2), 6, 23]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁷, 11, F₂, 2, 11) (dual of [(11, 2), 5, 12]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(2¹¹, 6, F₂, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
        dual of repetition NRT-code with length 6 [i]
  2. linear OOA(2²³, 12, F₂, 2, 22) (dual of [(12, 2), 1, 23]-NRT-code), using
    - strength reduction [i] based on linear OOA(2²³, 12, F₂, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
      - dual of repetition NRT-code with length 12 [i]
linear OOA(2⁴⁵, 23, F₂, 2, 45) (dual of [(23, 2), 1, 46]-NRT-code), using
- dual of repetition NRT-code with length 23 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁷⁶, 92, F₂, 2, 90) (dual of [(92, 2), 8, 91]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁷⁶, 92, F₂, 2, 91) (dual of [(92, 2), 8, 92]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs