MinT - Information on Result #1027111

Information on Result #1027111

Linear OOA(4²⁴⁴, 85, F₄, 3, 188) (dual of [(85, 3), 11, 189]-NRT-code), using juxtaposition based on

linear OOA(4⁶⁴, 25, F₄, 3, 54) (dual of [(25, 3), 11, 55]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁶⁴, 26, F₄, 3, 54) (dual of [(26, 3), 14, 55]-NRT-code), using
  - algebraic-geometric NRT-code AG(3;F,23P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁶⁹, 60, F₄, 3, 133) (dual of [(60, 3), 11, 134]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(4⁷⁹, 30, F₄, 3, 66) (dual of [(30, 3), 11, 67]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,23P) [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
    - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²⁴⁴, 85, F₄, 3, 187) (dual of [(85, 3), 11, 188]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁴⁴, 85, F₄, 3, 186) (dual of [(85, 3), 11, 187]-NRT-code)	[i]		Strength Reduction for OOAs