MinT - Information on Result #1129530

Information on Result #1129530

Linear OOA(2²⁵⁴, 79, F₂, 5, 99) (dual of [(79, 5), 141, 100]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁰¹, 37, F₂, 5, 49) (dual of [(37, 5), 84, 50]-NRT-code), using
- constructionÂ X applied to AG(5;F,110P) âŠ‚ AG(5;F,123P) [i] based on
  1. linear OOA(2⁸⁸, 32, F₂, 5, 49) (dual of [(32, 5), 72, 50]-NRT-code), using algebraic-geometric NRT-code AG(5;F,110P) [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(2⁷⁵, 32, F₂, 5, 36) (dual of [(32, 5), 85, 37]-NRT-code), using algebraic-geometric NRT-code AG(5;F,123P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33 (see above)
  3. linear OOA(2¹³, 5, F₂, 5, 12) (dual of [(5, 5), 12, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(5;F,12P) [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(2¹⁵³, 42, F₂, 5, 99) (dual of [(42, 5), 57, 100]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(5;F,110P) [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(2²⁵⁴, 79, F₂, 5, 98) (dual of [(79, 5), 141, 99]-NRT-code)	[i]		Strength Reduction for OOAs