MinT - Information on Result #1129478

Information on Result #1129478

Linear OOA(2²²⁰, 69, F₂, 5, 88) (dual of [(69, 5), 125, 89]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁸³, 33, F₂, 5, 44) (dual of [(33, 5), 82, 45]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(5;F,120P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹³⁷, 36, F₂, 5, 88) (dual of [(36, 5), 43, 89]-NRT-code), using
- constructionÂ X applied to AG(5;F,71P) âŠ‚ AG(5;F,81P) [i] based on
  1. linear OOA(2¹²⁷, 32, F₂, 5, 88) (dual of [(32, 5), 33, 89]-NRT-code), using algebraic-geometric NRT-code AG(5;F,71P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33 (see above)
  2. linear OOA(2¹¹⁷, 32, F₂, 5, 78) (dual of [(32, 5), 43, 79]-NRT-code), using algebraic-geometric NRT-code AG(5;F,81P) [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]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁰, 69, F₂, 5, 87) (dual of [(69, 5), 125, 88]-NRT-code)	[i]		Strength Reduction for OOAs