MinT - Information on Result #1129398

Information on Result #1129398

Linear OOA(3²³⁹, 79, F₃, 5, 117) (dual of [(79, 5), 156, 118]-NRT-code), using constructionÂ X based on

linear OOA(3²²⁴, 73, F₃, 5, 117) (dual of [(73, 5), 141, 118]-NRT-code), using OOA from sequence [i] based on digital (107, 73)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]
linear OOA(3²⁰⁹, 73, F₃, 5, 102) (dual of [(73, 5), 156, 103]-NRT-code), using OOA from sequence [i] based on digital (107, 73)-sequence over F₃ (see above)
linear OOA(3¹⁵, 6, F₃, 5, 14) (dual of [(6, 5), 15, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁵, 7, F₃, 5, 14) (dual of [(7, 5), 20, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,20P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, 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(3²³⁹, 79, F₃, 5, 116) (dual of [(79, 5), 156, 117]-NRT-code)	[i]		Strength Reduction for OOAs