MinT - Information on Result #1080447

Information on Result #1080447

Linear OOA(2¹⁸⁰, 76, F₂, 4, 58) (dual of [(76, 4), 124, 59]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁸, 34, F₂, 4, 29) (dual of [(34, 4), 68, 30]-NRT-code), using
- extracting embedded OOA [i] based on digital (39, 68, 34)-net over F₂, using
  - trace code for nets [i] based on digital (5, 34, 17)-net over F₄, using
    - net from sequence [i] based on digital (5, 16)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
        an explicitly constructive algebraic function field [i]
linear OOA(2¹¹², 42, F₂, 4, 58) (dual of [(42, 4), 56, 59]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,109P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, 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(2¹⁸⁰, 38, F₂, 7, 58) (dual of [(38, 7), 86, 59]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁸⁰, 38, F₂, 8, 58) (dual of [(38, 8), 124, 59]-NRT-code)	[i]		OOA Folding