MinT - Information on Result #1084409

Information on Result #1084409

Linear OOA(3²³¹, 69, F₃, 4, 137) (dual of [(69, 4), 45, 138]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁵⁸, 23, F₃, 4, 45) (dual of [(23, 4), 34, 46]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁵⁸, 24, F₃, 4, 45) (dual of [(24, 4), 38, 46]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,50P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]
linear OOA(3⁸¹, 23, F₃, 4, 68) (dual of [(23, 4), 11, 69]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁸¹, 24, F₃, 4, 68) (dual of [(24, 4), 15, 69]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,27P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24 (see above)
linear OOA(3⁹², 23, F₃, 4, 92) (dual of [(23, 4), 0, 93]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²³¹, 69, F₃, 4, 136) (dual of [(69, 4), 45, 137]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²³¹, 69, F₃, 4, 135) (dual of [(69, 4), 45, 136]-NRT-code)	[i]		Strength Reduction for OOAs