MinT - Information on Result #894647

Information on Result #894647

Linear OOA(2¹⁰¹, 54, F₂, 2, 53) (dual of [(54, 2), 7, 54]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁸, 27, F₂, 2, 26) (dual of [(27, 2), 6, 27]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²¹, 13, F₂, 2, 13) (dual of [(13, 2), 5, 14]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁸, 6, F₂, 2, 6) (dual of [(6, 2), 4, 7]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(2¹³, 7, F₂, 2, 13) (dual of [(7, 2), 1, 14]-NRT-code), using
        dual of repetition NRT-code with length 7 [i]
  2. linear OOA(2²⁷, 14, F₂, 2, 26) (dual of [(14, 2), 1, 27]-NRT-code), using
    - strength reduction [i] based on linear OOA(2²⁷, 14, F₂, 2, 27) (dual of [(14, 2), 1, 28]-NRT-code), using
      - dual of repetition NRT-code with length 14 [i]
linear OOA(2⁵³, 27, F₂, 2, 53) (dual of [(27, 2), 1, 54]-NRT-code), using
- dual of repetition NRT-code with length 27 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁰⁸, 108, F₂, 2, 107) (dual of [(108, 2), 8, 108]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs