MinT - Information on Result #1026817

Information on Result #1026817

Linear OOA(4²⁴², 87, F₄, 3, 176) (dual of [(87, 3), 19, 177]-NRT-code), using juxtaposition based on

linear OOA(4⁷⁴, 31, F₄, 3, 59) (dual of [(31, 3), 19, 60]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁷⁴, 32, F₄, 3, 59) (dual of [(32, 3), 22, 60]-NRT-code), using
  - algebraic-geometric NRT-code AG(3;F,36P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁴⁹, 56, F₄, 3, 116) (dual of [(56, 3), 19, 117]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,51P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
  - F₅ 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(4²⁴², 87, F₄, 3, 175) (dual of [(87, 3), 19, 176]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁴², 87, F₄, 3, 174) (dual of [(87, 3), 19, 175]-NRT-code)	[i]		Strength Reduction for OOAs