MinT - Information on Result #1080401

Information on Result #1080401

Linear OOA(2¹⁷¹, 78, F₂, 4, 53) (dual of [(78, 4), 141, 54]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³⁵, 12, F₂, 4, 26) (dual of [(12, 4), 13, 27]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,21P) [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹³⁶, 66, F₂, 4, 53) (dual of [(66, 4), 128, 54]-NRT-code), using
- extracting embedded OOA [i] based on digital (83, 136, 66)-net over F₂, using
  - trace code for nets [i] based on digital (15, 68, 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, 39, F₂, 7, 53) (dual of [(39, 7), 102, 54]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁷¹, 39, F₂, 8, 53) (dual of [(39, 8), 141, 54]-NRT-code)	[i]		OOA Folding