MinT - Information on Result #1027054

Information on Result #1027054

Linear OOA(4²¹⁶, 76, F₄, 3, 165) (dual of [(76, 3), 12, 166]-NRT-code), using juxtaposition based on

linear OOA(4⁴⁸, 20, F₄, 3, 41) (dual of [(20, 3), 12, 42]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁴⁸, 21, F₄, 3, 41) (dual of [(21, 3), 15, 42]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,21P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁵⁶, 56, F₄, 3, 123) (dual of [(56, 3), 12, 124]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,44P) [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(4²¹⁶, 76, F₄, 3, 164) (dual of [(76, 3), 12, 165]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²¹⁶, 76, F₄, 3, 163) (dual of [(76, 3), 12, 164]-NRT-code)	[i]		Strength Reduction for OOAs