MinT - Information on Result #1027366

Information on Result #1027366

Linear OOA(4¹⁶⁸, 58, F₄, 3, 138) (dual of [(58, 3), 6, 139]-NRT-code), using juxtaposition based on

linear OOA(4³³, 13, F₄, 3, 30) (dual of [(13, 3), 6, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4³³, 14, F₄, 3, 30) (dual of [(14, 3), 9, 31]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,11P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4¹²⁹, 45, F₄, 3, 107) (dual of [(45, 3), 6, 108]-NRT-code), using
- repeating each code word 3 times [i] based on linear OOA(4³⁹, 15, F₄, 3, 35) (dual of [(15, 3), 6, 36]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,9P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, 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(4¹⁶⁸, 58, F₄, 3, 137) (dual of [(58, 3), 6, 138]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4¹⁶⁸, 58, F₄, 3, 136) (dual of [(58, 3), 6, 137]-NRT-code)	[i]		Strength Reduction for OOAs