MinT - Information on Result #910696

Information on Result #910696

Linear OOA(9⁷⁹, 41, F₉, 2, 74) (dual of [(41, 2), 3, 75]-NRT-code), using juxtaposition based on

linear OOA(9²³, 13, F₉, 2, 22) (dual of [(13, 2), 3, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9²³, 16, F₉, 2, 22) (dual of [(16, 2), 9, 23]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
    - a function field by GarcÃa and Quoos [i]
linear OOA(9⁵³, 28, F₉, 2, 51) (dual of [(28, 2), 3, 52]-NRT-code), using
- standard lengthening with (d₀,â€¦,d₁)Â = (50,51) [i] based on linear OOA(9⁵¹, 27, F₉, 2, 49) (dual of [(27, 2), 3, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,4P) with known gap numbers [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using the Hermitian function field over F₉ [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(9⁷⁹, 41, F₉, 2, 73) (dual of [(41, 2), 3, 74]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(9⁷⁹, 41, F₉, 2, 72) (dual of [(41, 2), 3, 73]-NRT-code)	[i]		Strength Reduction for OOAs