MinT - Information on Result #1656445

Information on Result #1656445

Linear OOA(3²³¹, 89, F₃, 5, 145) (dual of [(89, 5), 214, 146]-NRT-code), using constructionÂ X applied to AG(5;F,269P) âŠ‚ AG(5;F,284P) based on

linear OOA(3²¹⁶, 83, F₃, 5, 145) (dual of [(83, 5), 199, 146]-NRT-code), using algebraic-geometric NRT-code AG(5;F,269P) [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
- algebraic function fields over â„¤₃ by Niederreiter/Xing [i]
linear OOA(3²⁰¹, 83, F₃, 5, 130) (dual of [(83, 5), 214, 131]-NRT-code), using algebraic-geometric NRT-code AG(5;F,284P) [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84 (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: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²³¹, 89, F₃, 5, 144) (dual of [(89, 5), 214, 145]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²³¹, 89, F₃, 5, 143) (dual of [(89, 5), 214, 144]-NRT-code)	[i]		Strength Reduction for OOAs