MinT - Information on Result #1049520

Information on Result #1049520

Linear OOA(3¹⁹⁴, 70, F₃, 3, 129) (dual of [(70, 3), 16, 130]-NRT-code), using juxtaposition based on

linear OOA(3⁸⁰, 32, F₃, 3, 59) (dual of [(32, 3), 16, 60]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,36P) [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3⁹⁸, 38, F₃, 3, 69) (dual of [(38, 3), 16, 70]-NRT-code), using
- constructionÂ X applied to AG(3;F,19P) âŠ‚ AG(3;F,21P) [i] based on
  1. linear OOA(3⁹⁵, 36, F₃, 3, 69) (dual of [(36, 3), 13, 70]-NRT-code), using algebraic-geometric NRT-code AG(3;F,19P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
  2. linear OOA(3⁹¹, 36, F₃, 3, 65) (dual of [(36, 3), 17, 66]-NRT-code), using algebraic-geometric NRT-code AG(3;F,21P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  3. linear OOA(3³, 2, F₃, 3, 3) (dual of [(2, 3), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3³, 3, F₃, 3, 3) (dual of [(3, 3), 6, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;6,3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁹⁴, 70, F₃, 3, 128) (dual of [(70, 3), 16, 129]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁹⁴, 70, F₃, 3, 127) (dual of [(70, 3), 16, 128]-NRT-code)	[i]		Strength Reduction for OOAs