MinT - Information on Result #1656447

Information on Result #1656447

Linear OOA(3²²⁹, 89, F₃, 5, 143) (dual of [(89, 5), 216, 144]-NRT-code), using constructionÂ X applied to AG(5;F,271P) âŠ‚ AG(5;F,286P) based on

linear OOA(3²¹⁴, 83, F₃, 5, 143) (dual of [(83, 5), 201, 144]-NRT-code), using algebraic-geometric NRT-code AG(5;F,271P) [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(3¹⁹⁹, 83, F₃, 5, 128) (dual of [(83, 5), 216, 129]-NRT-code), using algebraic-geometric NRT-code AG(5;F,286P) [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(3²²⁹, 89, F₃, 5, 142) (dual of [(89, 5), 216, 143]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²²⁹, 89, F₃, 5, 141) (dual of [(89, 5), 216, 142]-NRT-code)	[i]		Strength Reduction for OOAs