MinT - Information on Result #1026447

Information on Result #1026447

Linear OOA(3¹⁴⁷, 51, F₃, 3, 114) (dual of [(51, 3), 6, 115]-NRT-code), using juxtaposition based on

linear OOA(3³⁰, 12, F₃, 3, 26) (dual of [(12, 3), 6, 27]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,9P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹¹¹, 39, F₃, 3, 87) (dual of [(39, 3), 6, 88]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3²⁷, 11, F₃, 3, 23) (dual of [(11, 3), 6, 24]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3²⁷, 12, F₃, 3, 23) (dual of [(12, 3), 9, 24]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,12P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12 (see above)
  2. linear OOA(3⁷⁸, 28, F₃, 3, 63) (dual of [(28, 3), 6, 64]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,20P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, 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(3¹⁴⁷, 51, F₃, 3, 113) (dual of [(51, 3), 6, 114]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁴⁷, 51, F₃, 3, 112) (dual of [(51, 3), 6, 113]-NRT-code)	[i]		Strength Reduction for OOAs