MinT - Information on Result #1084614

Information on Result #1084614

Linear OOA(3²²³, 81, F₃, 4, 104) (dual of [(81, 4), 101, 105]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁴⁹, 27, F₃, 4, 34) (dual of [(27, 4), 59, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁴⁹, 28, F₃, 4, 34) (dual of [(28, 4), 63, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,77P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3⁶⁷, 27, F₃, 4, 52) (dual of [(27, 4), 41, 53]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁶⁷, 28, F₃, 4, 52) (dual of [(28, 4), 45, 53]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,59P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
linear OOA(3¹⁰⁷, 27, F₃, 4, 104) (dual of [(27, 4), 1, 105]-NRT-code), using
- strength reduction [i] based on linear OOA(3¹⁰⁷, 27, F₃, 4, 107) (dual of [(27, 4), 1, 108]-NRT-code), using
  - dual of repetition NRT-code with length 27 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²²³, 81, F₃, 4, 103) (dual of [(81, 4), 101, 104]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²²³, 81, F₃, 4, 102) (dual of [(81, 4), 101, 103]-NRT-code)	[i]		Strength Reduction for OOAs