MinT - Information on Result #1080366

Information on Result #1080366

Linear OOA(2¹⁶¹, 74, F₂, 4, 51) (dual of [(74, 4), 135, 52]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁹, 8, F₂, 4, 25) (dual of [(8, 4), 3, 26]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,6P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹³², 66, F₂, 4, 51) (dual of [(66, 4), 132, 52]-NRT-code), using
- extracting embedded OOA [i] based on digital (81, 132, 66)-net over F₂, using
  - trace code for nets [i] based on digital (15, 66, 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(2¹⁶¹, 37, F₂, 8, 51) (dual of [(37, 8), 135, 52]-NRT-code)	[i]		OOA Folding