MinT - Information on Result #1093594

Information on Result #1093594

Linear OOA(2¹⁶⁵, 74, F₂, 4, 53) (dual of [(74, 4), 131, 54]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁹, 8, F₂, 4, 26) (dual of [(8, 4), 3, 27]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2⁹, 3, F₂, 4, 9) (dual of [(3, 4), 3, 10]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(4;3,2) [i]
  2. linear OOA(2¹⁷, 5, F₂, 4, 16) (dual of [(5, 4), 3, 17]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁶⁵, 37, F₂, 8, 53) (dual of [(37, 8), 131, 54]-NRT-code)	[i]		OOA Folding