MinT - Information on Result #1129474

Information on Result #1129474

Linear OOA(2²³³, 78, F₂, 5, 87) (dual of [(78, 5), 157, 88]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁹², 36, F₂, 5, 43) (dual of [(36, 5), 88, 44]-NRT-code), using
- constructionÂ X applied to AG(5;F,116P) âŠ‚ AG(5;F,126P) [i] based on
  1. linear OOA(2⁸², 32, F₂, 5, 43) (dual of [(32, 5), 78, 44]-NRT-code), using algebraic-geometric NRT-code AG(5;F,116P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁷², 32, F₂, 5, 33) (dual of [(32, 5), 88, 34]-NRT-code), using algebraic-geometric NRT-code AG(5;F,126P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33 (see above)
  3. linear OOA(2¹⁰, 4, F₂, 5, 9) (dual of [(4, 5), 10, 10]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2¹⁰, 5, F₂, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,10P) [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(2¹⁴¹, 42, F₂, 5, 87) (dual of [(42, 5), 69, 88]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(5;F,122P) [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(2²³³, 78, F₂, 5, 86) (dual of [(78, 5), 157, 87]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²³⁴, 78, F₂, 5, 87) (dual of [(78, 5), 156, 88]-NRT-code)	[i]		OOA Duplication