MinT - Information on Result #1080412

Information on Result #1080412

Linear OOA(2¹⁷¹, 76, F₂, 4, 54) (dual of [(76, 4), 133, 55]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³³, 10, F₂, 4, 27) (dual of [(10, 4), 7, 28]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,12P) [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(2¹³⁸, 66, F₂, 4, 54) (dual of [(66, 4), 126, 55]-NRT-code), using
- extracting embedded OOA [i] based on digital (84, 138, 66)-net over F₂, using
  - trace code for nets [i] based on digital (15, 69, 33)-net over F₄, using
    - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, 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(2¹⁷¹, 38, F₂, 7, 54) (dual of [(38, 7), 95, 55]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁷¹, 38, F₂, 8, 54) (dual of [(38, 8), 133, 55]-NRT-code)	[i]		OOA Folding