MinT - Information on Result #1129527

Information on Result #1129527

Linear OOA(2²⁵², 79, F₂, 5, 98) (dual of [(79, 5), 143, 99]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁸⁸, 33, F₂, 5, 49) (dual of [(33, 5), 77, 50]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(5;F,115P) [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(2¹⁶⁴, 46, F₂, 5, 98) (dual of [(46, 5), 66, 99]-NRT-code), using
- constructionÂ X applied to AG(5;F,18P) âŠ‚ AG(5;F,20P) [i] based on
  1. linear OOA(2¹⁵⁵, 42, F₂, 5, 101) (dual of [(42, 5), 55, 102]-NRT-code), using algebraic-geometric NRT-code AG(5;F,18P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹⁴³, 42, F₂, 5, 89) (dual of [(42, 5), 67, 90]-NRT-code), using algebraic-geometric NRT-code AG(5;F,20P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42 (see above)
  3. linear OOA(2⁹, 4, F₂, 5, 8) (dual of [(4, 5), 11, 9]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2⁹, 5, F₂, 4, 8) (dual of [(5, 4), 11, 9]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,11P) [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(2²⁵², 79, F₂, 5, 97) (dual of [(79, 5), 143, 98]-NRT-code)	[i]		Strength Reduction for OOAs